Quantum plasmadynamics: unmagnetized plasmas
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| Sprache: | English |
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| Schriftenreihe: | Lecture notes in physics
735 |
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| Beschreibung: | XXI, 464 S. graph. Darst. |
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| 020 | |a 9780387739021 |9 978-0-387-73902-1 | ||
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| 049 | |a DE-384 |a DE-11 |a DE-703 | ||
| 084 | |a UD 8220 |0 (DE-625)145543: |2 rvk | ||
| 100 | 1 | |a Melrose, Donald B. |d 1940- |e Verfasser |0 (DE-588)172255007 |4 aut | |
| 245 | 1 | 0 | |a Quantum plasmadynamics |b unmagnetized plasmas |c Donald B. Melrose |
| 264 | 1 | |a New York, NY |b Springer |c 2008 | |
| 300 | |a XXI, 464 S. |b graph. Darst. | ||
| 490 | 1 | |a Lecture notes in physics |v 735 | |
| 650 | 0 | 7 | |a Quantenelektrodynamik |0 (DE-588)4047982-1 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Plasmadynamik |0 (DE-588)4123952-0 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Quantenelektrodynamik |0 (DE-588)4047982-1 |D s |
| 689 | 0 | 1 | |a Plasmadynamik |0 (DE-588)4123952-0 |D s |
| 689 | 0 | |5 DE-604 | |
| 830 | 0 | |a Lecture notes in physics |v 735 |w (DE-604)BV000003166 |9 735 | |
| 856 | 4 | 2 | |m Digitalisierung UB Augsburg |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016295461&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-016295461 | ||
Datensatz im Suchindex
| _version_ | 1804137346290941952 |
|---|---|
| adam_text | Contents
Preface
........................................................
V
1
Response 4-tensors
........................................ 1
1.1
4-tensor
notation
........................................ 2
1.1.1
4-tensor
equations
................................. 2
1.1.2
Important
4-
vectors
...............................
З
1.1.3
Lorentz
transformations
............................ 4
1.1.4
Specific transformation matrices
..................... 5
1.2
Electromagnetic field
..................................... 7
1.2.1
Maxwell s equations
............................... 7
1.2.2
Electric and magnetic field 4-vectors
................. 8
1.2.3
Invariants of the electromagnetic field
................ 9
1.2.4
Continuity equations
............................... 10
1.2.5
Gauge transformations
............................. 10
1.3
Fourier transforms
....................................... 12
1.3.1
4-dimensional Fourier transform
..................... 12
1.3.2
Truncations and the Dirac ¿-functions
............... 13
1.3.3
Fourier transforms of the step and sign functions
...... 14
1.3.4
Plemelj formula
................................... 15
1.3.5
Confinement to the forward light cone
............... 15
1.4
Linear and nonlinear response 4-tensors
.................... 17
1.4.1
Induced current
................................... 17
1.4.2
Weak-turbulence expansion
......................... 17
1.4.3
Reality condition
.................................. 18
1.4.4
Charge-continuity and gauge-invariance
.............. 18
1.4.5
Separation into dissipative and nondissipative parts
.... 19
1.4.6
Kramers-Kronig relations
........................... 19
1.4.7
Onsager relations
.................................. 20
1.4.8
Nonlinear response tensors
.......................... 21
1.5
Alternative descriptions of the linear response
............... 24
1.5.1
Alternative form of Maxwell s equations
.............. 24
χ
Contents
1.5.2
Response 3-tensors
for the
static response
............ 24
1.5.3
Covariant
form for the
static response
................ 25
1.5.4
Generalizations of phenomenological electrodynamics
.. 26
1.5.5
Alternative form for the linear response
.............. 27
1.5.6
Conductivity 4-tensor
.............................. 28
1.5.7
Response 3-tensors for plasmas
...................... 28
1.5.8
Construction of the 4-tensor from the 3-tensor
........ 29
1.6 Isotropie
media
......................................... 30
1.6.1
Covariant description of an
isotropie
medium
......... 30
1.6.2
Construction of L^(k,u),T^{k,u), R»u{k,u)
........ 31
1.6.3
Construction of nL(k),
Пт{к), Пн{к)...............
32
1.6.4
Static limit for an
isotropie
plasma
.................. 33
1.7
Response tensors for simple media
......................... 34
1.7.1
Cold unmagnetized plasma
......................... 34
1.7.2
Isotropie
dielectrics
................................ 35
1.7.3
Isotropie nonrelativistic
thermal plasma
.............. 35
References
.................................................. 36
2
Covariant theory of wave dispersion
....................... 37
2.1
Wave equation and the photon propagator
.................. 38
2.1.1
Wave equation
.................................... 38
2.1.2
Homogeneous wave equation
........................ 38
2.1.3
Photon propagator
................................ 39
2.1.4
Formal construction of the propagator
............... 39
2.1.5
Temporal gauge
................................... 41
2.1.6 Lorenz
gauge
..................................... 41
2.1.7
Photon propagator in
vacuo
........................ 42
2.2
Evaluation of (k) and X^aT(k)
........................... 43
2.2.1
Arbitrary
4x4
matrices
........................... 43
2.2.2
Cayley-Hamilton theorem
.......................... 44
2.2.3
Traces of
Аџџ
..................................... 45
2.2.4
Dispersion equation in terms of 3-tensor components
... 46
2.2.5
Relation between 3-tensor and 4-tensor formalisms
.... 47
2.3
Dispersion relations and polarization 4-vectors
.............. 48
2.3.1
Dispersion equation
................................ 48
2.3.2
Inclusion of weak dissipation
........................ 49
2.3.3
Antihermitian part of the photon propagator
......... 49
2.3.4
Polarization 4-vectors
.............................. 50
2.3.5
Normalization of polarization 4-vectors
............... 51
2.3.6
Ratio of electric to total energy
..................... 51
2.3.7
Alternative forms for R^j(k)
........................ 52
2.4
Wave damping and wave energetics
........................ 54
2.4.1
Wave amplitude and wave energy
.................... 54
2.4.2
Electromagnetic contributions to the wave energy
..... 55
2.4.3
Wave action
...................................... 55
2.4.4
Work done by the dissipative part
of the linear response
..............
2 4 5
Absorption coefficient
.............
2І4.6
Continuity equation for wave energy^
56
57
57
58
2.4.7
Interpretation of the energy-momentum tensor
........
uo
2.5
Waves in
isotropie
and weakly anisotropic media
............ 59
2.5.1
Longitudinal and transverse waves
................... 59
2.5.2
Polarization 4-vector for longitudinal waves
........... 60
2.5.3
Transverse waves in optically active media
............ 60
2.5.4
Degenerate transverse wave modes
................... 61
2.5.5
Polarization of transverse waves
..................... 62
2.5.6
Sum over transverse states of polarization
............ 63
2.5.7
Transverse waves in weakly anisotropic media
......... 64
2.5.8
Transfer equation for polarized radiation
............. 65
2.5.9
Stokes parameters
................................. 67
2.6
Lorentz
transformation of wave properties
.................. 69
2.6.1
Transformation of the wave 4-vector
................. 69
2.6.2
Longitudinal waves in a nonrelativistic
thermal plasma
................................... 70
2.6.3
Langmuir waves in a moving frame
.................. 71
2.6.4
Transverse waves in a moving frame
................. 72
2.6.5
Transformation of wave energetics
................... 73
2.6.6
Transformation of Rm
............................. 74
References
.................................................. 75
3
Particle and wave subsystems
.............................. 77
3.1
Covariant Lagrangians for free particles and fields
........... 78
3.1.1
Lagrangian density
................................ 78
3.1.2
Orbit of the particle
............................... 79
3.1.3
Perturbation expansion in A{k)
..................... 80
3.1.4
Lagrangian density for a particle system
.............. 80
3.1.5
Euler-Lagrange equations for a field
................. 81
3.1.6
Lagrangian density for the electromagnetic field
....... 82
3.2
Background and wave subsystems
......................... 83
3.2.1
Forward-scattering approach
........................ 83
3.2.2
Vlasov
approach
.................................. 83
3.2.3
Expansion about oscillation-center coordinates
........ 84
3.2.4
Expansion of the Lagrangian
........................ 85
3.2.5
Second-order Lagrangian in fc-space
.................. 86
3.2.6
Nonlinear Lagrangian
.............................. 87
3.2.7
Ponderomotive force
............................... 88
3.3
Forward-scattering method
............................... 90
3.3.1
Single particle current
............................. 90
3.3.2
Perturbation expansion for an unmagnetized plasma
... 90
3.3.3
Forward-scattering assumption
...................... 92
ЛИ
Contents
3.4
Cold plasma model
...................................... 93
3.4.1
Covariant fluid equations
........................... 93
3.4.2
Perturbation expansion of the fluid equations
......... 93
3.4.3
First and second order currents
..................... 95
3.4.4
Response tensors for a cold unmagnetized plasma
..... 95
3.5
Covariant
Vlasov
theory
.................................. 97
3.5.1
Statistical theory of plasmas
........................ 97
3.5.2
Boltzmann equation
............................... 98
3.5.3
Boltzmann equation in 8-dimensional phase space
..... 99
3.5.4
Fluctuations in a plasma
...........................100
3.5.5
Two-scale separation of the distribution function
......101
3.5.6
Fluctuations for undressed particles
..................102
3.5.7
Fluctuations in the current
.........................102
3.5.8
Fluctuations in the electromagnetic field
.............103
3.6
Lagrangian description of a wave subsystem
................104
3.6.1
Lagrangian density a wave subsystem
................104
3.6.2
Euler-Lagrange equations for a wave subsystem
.......105
3.6.3
Energy-momentum tensor Tfif{k)
...................105
3.6.4
Inclusion of emission and absorption
.................106
3.6.5
Lorentz
transformation of Tj^(fc)
....................106
3.6.6
Energy-momentum tensor for static fields
.............106
3.7
Covariant theory of ray propagation
.......................108
3.7.1
Wave Hamiltonian
.................................108
3.7.2
Eikonal approach
..................................109
3.7.3
Illustrative example: transverse waves
................110
3.7.4
Curved space-time
.................................110
3.7.5
Ray equations in curved space-time
..................
Ill
3.7.6
Cold plasma in
a
Schwarzschild
metric
...............112
3.7.7
Rays in a rotating coordinate frame
..................113
References
..................................................115
4
Dispersion in relativistic plasmas
..........................117
4.1
Linear response for an
isotropie
plasma
.....................118
4.1.1
General expressions for the linear response tensor
......118
4.1.2
Antihermitian part
................................118
4.1.3
Number densities and plasma frequencies
.............119
4.1.4
Response for an
isotropie
plasma
....................120
4.1.5
Vlasov
form for an
isotropie
plasma
..................122
4.2
Relativistic thermal distribution
...........................123
4.2.1
Jiittner distribution
................................123
4.2.2
Properties of Kv{x)
................................124
4.2.3
Average quantities
.................................125
4.3
Linear response of a relativistic thermal plasma
.............127
4.3.1
Relativistic plasma dispersion function T{z,p)
........127
4.3.2
Derivation by the forward-scattering method
..........127
Contents
лій
4.3.3
Derivation by the
Vlasov
approach
..................128
4.3.4
SLlin s
method
..-..................................129
4.3.5
Trubnikov s integral
...............................130
4.3.6
Longitudinal and transverse parts
...................133
4.4
Relativistic plasma dispersion functions (RPDPs)
............135
4.4.1
Definitions of plasma dispersion functions
............135
4.4.2
Real and imaginary parts of Trubnikov functions
......135
4.4.3
Properties of
Т(г,
p)
and
T (z, p)
....................138
4.4.4
Longitundinal
and transverse response functions
.......140
4.4.5
Expansion for
z2 <
1..............................141
4.4.6
Expansion for z2
> 1..............................142
4.4.7
Weakly relativistic limit
............................143
4.4.8
Nonrelativistic limit
...............................143
4.4.9
Ultrarelativistic limit
..............................144
4.4.10
Generalized Trubnikov functions
....................144
4.5
Waves in relativistic thermal plasmas
......................147
4.5.1
General dispersion relations
.........................147
4.5.2
Debye length
.....................................147
4.5.3
Cutoff frequencies for
г2
» 1 .......................148
4.5.4
Dispersion curves for Langmuir waves
................149
4.5.5
Approximate dispersion relations for Langmuir waves
.. 150
4.5.6
Landau damping
..................................151
4.5.7
Transverse waves
..................................152
4.5.8
Acoustic waves
....................................153
4.6
Instability due to anisotropic distributions
..................155
4.6.1
Classes of anisotropic distributions
..................155
4.6.2
Distributions with relative streaming
.................156
4.6.3
Strictly-parallel thermal distribution
.................156
4.6.4
Trubnikov s method for strictly-parallel distribution
.. . 158
4.6.5
Strictly-perpendicular thermal distribution
...........159
4.7
Nonlinear response tensors
................................162
4.7.1
General forms for the nonlinear response tensors
......162
4.7.2
Alternative forms derived using the
Vlasov
approach
... 162
4.7.3
Linear response for a longitudinal slow disturbance
.... 163
4.7.4
Nonlinear responses with one slow disturbance
........164
4.7.5
Electrostatic model
................................165
4.7.6
Two fast and two slow disturbances
..................166
References
..................................................167
5
Classical plasmadynamics
..................................169
5.1
Spontaneous emission
....................................170
5.1.1
Radiation field
....................................170
5.1.2 4-
momentum radiated
..............................171
5.1.3
Probability of emission
.............................172
5.1.4
Probability for Cerenkov emission
...................172
XIV Contents
5.1.5
Cerenkov
condition
................................173
5.1.6
Quantum
recoil
...................................174
5.2 Quasilinear
equations
....................................175
5.2.1
Detailed balance
..................................175
5.2.2
Transfer equation for waves
.........................175
5.2.3 Quasilinear
equation for particles
....................177
5.2.4
Conservation of 4-momentum
.......................178
5.2.5
Interpretation of the
quasilinear
diffusion coefficients
... 179
5.2.6
Radiation reaction force
............................179
5.2.7
Quantum recoil in spontaneous emission
..............180
5.2.8
Covariant Fokker-Planck equation
...................181
5.2.9
Second Fokker-Planck coefficient
....................181
5.2.10
First Fokker-Planck coefficient
......................182
5.3
Specific emission processes
................................184
5.3.1
Power radiated in Cerenkov emission
.................184
5.3.2
Appearance emission
...............................185
5.3.3
Transition radiation
...............................186
5.3.4
Electron-ion collisions
..............................186
5.3.5
Bremsstrahlung: the impulsive model
................187
5.3.6
Bremsstrahlung: the straight line approximation
.......189
5.4
Fluctuations and the collision integral
......................192
5.4.1
Form of the collision integral
........................192
5.4.2
Kinetic equation due to fluctuations
.................193
5.4.3
Inclusion of the self-consistent field
..................193
5.4.4 Quasilinear
equation
...............................194
5.4.5
Collision integral
..................................195
5.4.6
Fluctuations in an
isotropie
plasma
..................196
5.4.7
Scattering probability in an
isotropie
plasma
..........196
5.4.8
Collisions involving nonrelativistic particles
...........197
5.4.9
Electron-electron collisions in a relativistic plasma
.....198
5.5
Scattering of waves by particles
...........................200
5.5.1
Current associated with scattering
...................200
5.5.2
Probability for scattering
...........................201
5.5.3
Kinetic equations for scattering
.....................202
5.5.4
Double emission and double absorption
..............204
5.5.5
Interference between Thomson and nonlinear
scattering
........................................205
5.5.6
Virtual longitudinal and transverse waves
............206
5.6
Thomson and inverse Compton scattering
..................207
5.6.1
Thomson scattering in
vacuo
........................207
5.6.2
Scattering of an
isotropie
distribution of photons
......208
5.6.3
Scattering kernel
..................................209
5.6.4
Exact results for Thomson scattering
................211
5.6.5
Kinetic equation for
isotropie
particles and photons
.... 212
5.6.6
Kompaneets equation
..............................212
Contents XV
5.6.7
Inverse Compton scattering
.........................214
5.6.8
Induced scattering by relativistic electrons
............215
5.7
Wave-wave interactions
...................................217
5.7.1
Three-wave interactions
............................217
5.7.2
Probability for a three-wave interaction
..............217
5.7.3
Kinetic equations for three-wave processes
............219
5.7.4
Current for four-wave interactions
...................219
5.7.5
Effective cubic response
............................221
5.7.6
Four-wave interactions
.............................221
5.7.7
Kinetic equations for three-wave coalescence
..........222
5.7.8
Kinetic equations for wave-wave scattering
............223
5.7.9
Phase-coherent interactions
.........................223
5.8
Nonlinear wave equations
.................................226
5.8.1
Nonlinear correction to the linear response
............226
5.8.2
Nonlinear effects involving two different wave modes
... 226
5.8.3
Nonlinear damping processes
........................227
5.8.4
Nonlinearity involving a single wave mode
............229
5.8.5
Zakharov equations
................................230
References
..................................................232
6
Quantum field theory
......................................233
6.1
Relativistic wave equations
...............................234
6.1.1
State functions and operators in a Hilbert space
.......234
6.1.2
Link between classical and quantum descriptions
......235
6.1.3
Pictures of the time evolution
.......................235
6.1.4
Representations
...................................236
6.1.5
Klein-Gordon equation
.............................237
6.1.6
Dirac equation
....................................238
6.1.7
Covariant form of Dirac s equation
..................238
6.1.8
Dirac Hamiltonian
.................................239
6.1.9
Standard representation
............................240
6.1.10
Dirac matrices
σμι>
and 75
..........................241
6.1.11
Basic set of Dirac matrices
.........................241
6.1.12
Traces of products of 7-matrices
.....................242
6.2
Wavefunctions for relativistic particles
.....................243
6.2.1
Generic solutions
..................................243
6.2.2
Plane wavefunctions
...............................244
6.2.3
Solutions in the standard representation
..............245
6.2.4
Orthogonality and completeness relations
.............245
6.2.5
Wavefunctions us(p), va(p)
.........................246
6.2.6
Neutrinos
........................................246
6.3
Lagrangian formulation
..................................248
6.3.1
Klein-Gordon Lagrangian
...........................248
6.3.2
Dirac Lagrangian
..................................248
6.3.3
Particle action and occupation numbers
..............249
6.3.4
Inclusion
of an electromagnetic field
.................250
6.3.5
Magnetic moment of the electron
....................251
6.3.6
Interaction between Dirac and EM fields
.............251
6.3.7
Interaction between Klein-Gordon and EM fields
......252
6.4
Second quantization
.....................................253
6.4.1
Harmonic oscillator
................................253
6.4.2
Quantization of fields
..............................254
6.4.3
Anticommutation relations
for fermion fields
..........255
6.4.4
Quantization of fermion fields
.......................256
6.4.5
Normal ordering
..................................257
6.5
Propagators
............................................258
6.5.1
Solution of inhomogeneous wave equation
............258
6.5.2
Feynman contour
..................................259
6.5.3
Chronological operator
.............................260
6.5.4
Vacuum expectation value
..........................260
6.5.5
Electron propagator as a vacuum expectation value
.... 261
6.5.6
Contractions
......................................262
6.5.7
Boson propagator
.................................262
6.5.8
Photon propagator as a vacuum expectation value
.....263
6.6
Scattering matrix (5-matrix)
..............................264
6.6.1
Interaction picture
.................................264
6.6.2
Evolution of
Š
....................................265
6.6.3
Interaction Hamiltonian in QED
....................265
6.6.4
Initial and final states
..............................266
6.6.5
Scattering amplitudes
7}¡
and Ma
...................266
6.6.6
Additional interaction terms
........................267
6.6.7
Nonlinear responses in QPD
........................268
6.6.8
Interaction Hamiltonian in
SED.....................269
6.7
Elements in Feynman diagrams
...........................270
6.7.1
Connected and disjoint diagrams
....................270
6.7.2
First order diagrams in QED
.......................271
6.7.3
Crossed diagrams
..................................273
6.7.4
Multiple-photon vertices
...........................273
6.7.5
Second-order processes
.............................274
6.7.6
Propagators
......................................275
6.7.7
Loop momentum
..................................275
6.7.8
External fields
....................................276
6.7.9
Vertex formalism
..................................276
6.7.10
Momentum-space representation
....................277
References
..................................................278
7
QPD processes
............................................279
7.1
Rules for Feynman diagrams
.............................. 280
7.1.1
Rules for drawing diagrams
.........................280
7.1.2
Rules for constructing
Sa
...........................281
7.1.3
Rules for momentum space representations
...........282
7.1.4
Rules for the vertex formalism and for
SED...........283
7.1.5
Rules for weak interactions
.........................284
7.2
First-order processes
.....................................286
7.2.1
Conservation of 4-momentum
.......................286
7.2.2
Transition rate for Cerenkov emission
................286
7.2.3
Probability of Cerenkov emission
....................288
7.2.4
Cerenkov emission by an unpolarized electron
.........289
7.2.5
Kinetic equations for Cerenkov emission
..............290
7.2.6
Kinetic equation for the particles
....................291
7.2.7
Power radiated in transverse waves
..................291
7.2.8
One-photon pair creation
...........................292
7.2.9
Kinetic equations for one-photon pair creation
........292
7.3
Scattering processes
..................................... 294
7.3.1
Invariant kinematics
...............................294
7.3.2
Mandelstam
diagram
..............................296
7.3.3
Scattering cross section
............................296
7.3.4
Application to Compton scattering
..................299
7.4
Compton scattering and related processes
..................300
7.4.1
Compton scattering and nonlinear scattering
..........300
7.4.2
Derivation using the vertex formalism
................301
7.4.3
Probability for Compton scattering
..................302
7.4.4
Kinetic equations for Compton scattering
.............302
7.4.5
Compton scattering in
vacuo
........................303
7.4.6
Corrections for Compton scattering in a plasma
.......304
7.4.7
Compton scattering of unpolarized photons
...........305
7.4.8
Compton cross section
.............................305
7.4.9
Klein-Nishina cross section
.........................306
7.5
Mot-t scattering and bremsstrahlung
.......................308
7.5.1
Scattering of an electron by a Coulomb field
..........308
7.5.2
Mott
scattering
...................................308
7.5.3
Mott
cross section
.................................309
7.5.4
Bremsstrahlung in
Mott
scattering
..................310
7.5.5
Bremsstrahlung emission of soft photons
.............311
7.6
Electron-electron scattering
...............................314
7.6.1
Probability for M0ller scattering
.....................314
7.6.2
Dependence on momentum transfer
..................315
7.6.3
Kinetic equation for M0ller scattering
................316
7.6.4
M0ller scattering
in vacuo
..........................316
7.6.5
Bhabha scattering
.................................318
7.6.6
Small-angle M0ller scattering in a plasma
............319
7.6.7
Scattering in relativistic degenerate plasma
...........320
References
..................................................321
Responses of a quantum plasma
...........................323
8.1
Renormalization and regularization
........................324
8.1.1
Divergent diagrams
................................324
8.1.2
Vacuum polarization
...............................324
8.1.3
Regularization of the vacuum polarization tensor
......326
8.1.4
Effect of the vacuum polarization
on a Coulomb field
................................328
8.1.5
Cubic response tensor for the vacuum
................328
8.1.6
Dimensional restrictions on higher order responses
.....330
8.1.7
Mass operator
....................................331
8.1.8
Vertex correction and the Ward identity
..............332
8.2
Statistical average over a plasma
..........................334
8.2.1
Density matrix
....................................334
8.2.2
Statistical averages
................................334
8.2.3
Statistically averaged propagators
...................335
8.2.4
Spin dependence of the averaged propagator
..........336
8.2.5
Statistically averaged photon propagator
.............337
8.2.6
Forward scattering and cuts in closed loops
...........337
8.2.7
Unitarity
.........................................338
8.2.8
Linear and nonlinear responses
......................339
8.2.9
Macrosocpic mass renormalization
...................340
8.3
General forms for linear response tensor
....................341
8.3.1
Linear response tensor
.............................341
8.3.2
Alternative forms for
Пџџ{к)
.......................341
8.3.3
Electron and positron contributions
..................342
8.3.4
Charge-symmetric form
............................343
8.3.5
Antihermitian part of the response tensor
............343
8.3.6
Resonance conditions
..............................344
8.3.7
Quantum recoil
...................................345
8.3.8
Solutions of the resonance conditions
................346
8.3.9
Allowed resonances
................................347
8.4
Wigner matrix and density matrix approaches
...............349
8.4.1
Quasi-probability distribution
.......................349
8.4.2
Covariant Wigner matrix
...........................350
8.4.3
Basis set of covariant Wigner functions
...............351
8.4.4
First order Wigner functions
........................352
8.4.5
Linear response tensor from the Wigner matrix
.......352
8.4.6
Fluctuations in a quantum plasma
...................353
8.4.7
Fluctuations in the Wigner matrix
...................354
8.4.8
Fluctuations in the 4-current
........................355
8.4.9
Kubo s formula
...................................355
8.4.10
Density matrix approach
...........................356
8.4.11
Expansion of the density matrix
.....................357
8.4.12
Linear response tensor
.............................357
8.5
Nonlinear response tensors
................................359
8.5.1
Closed particle loops
...............................359
8.5.2
nth order nonlinear response tensor
..................359
8.5.3
Quadratic response tensor for an electron gas
.........360
8.5.4
Cubic response tensor for an electron gas
.............361
8.6
Inclusion of a photon gas
.................................363
8.6.1
Linear response due to a photon gas
.................363
8.6.2
Relation to three-wave coupling
.....................365
8.6.3
Instability due to a photon beam
....................365
8.6.4
Nonlinear effects of a photon gas
....................366
8.6.5
Dissipation modified by a photon gas
................367
8.6.6
Turbulent bremsstrahlung
..........................368
References
..................................................369
9
Isotropie
quantum plasmas
................................371
9.1
Isotropie
distributions
....................................372
9.1.1
Separation into longitudinal and transverse parts
......372
9.1.2
Isotropie
distribution in its rest frame
................373
9.1.3
Tsytovich s form for
Пь т{к)
.......................374
9.1.4
Integral over angles
...............................375
9.1.5
Relativistic quantum dispersion functions
.............376
9.1.6
Nonquantum limit
................................. 377
9.1.7
Fermi-Dirac distribution
............................377
9.2
Dissipation in
isotropie
quantum plasmas
...................378
9.2.1
Boundary of the resonance regions
...................378
9.2.2
Alternative forms of
Λχ
,
Л2.........................
379
9.2.3
Imaginary parts of the plasma dispersion functions
.... 379
9.2.4
Imaginary parts of the tfL(fc),
Пт(к)................
381
9.3
Linear response of a degenerate plasma
.....................382
9.3.1
Degenerate limit
..................................382
9.3.2
Evaluation of specific integrals
......................383
9.3.3
RQPDFs in the completely degenerate limit
..........384
9.3.4
Jancovici s response functions
.......................385
9.3.5
Dissipation due to LD and PC
......................386
9.3.6
Neglect of the quantum recoil
.......................387
9.3.7
Lindhard s response tensor
.........................388
9.4
Linear response of
a nondegenerate
plasma
.................390
9.4.1
Nondegenerate
limit
...............................390
9.4.2
Dispersion functions in the nondegenerate limit
.......391
9.4.3
Evaluation in terms of T{v, p)
.......................391
9.4.4
Dispersion functions for nondegenerate plasma
........392
9.4.5
Nonquantum limit
.................................393
9.4.6
Lowest order quantum corrections
...................393
9.4.7
High temperature limit
.............................394
9.4.8
Nearly
nondegenerate
limit
.........................394
9.5
Dispersion in
isotropie
plasmas
............................396
9.5.1
Debye-like screening
...............................396
9.5.2
Friedel oscillations in relativistic degenerate plasmas
... 396
9.5.3
Magnetic susceptibility of an electron gas
.............398
9.5.4
Cutoff frequency
..................................398
9.5.5
Waves in
nondegenerate
thermal plasmas
.............400
9.6
Waves in completely degenerate electron gas
................402
9.6.1
Langmuir waves in degenerate electron gas
...........402
9.6.2
Longitudinal response function
......................403
9.6.3
Longitudinal waves including relativistic effects
.......406
9.6.4
Superdense
plasmas
...............................407
References
..................................................408
10
Spin, MMR and neutrino plasma
..........................409
10.1
Spin operators and eigenfunctions
.........................410
10.1.1
Conserved quantities and constants of the motion
.....410
10.1.2
Spin operators
....................................411
10.1.3
Preferred spin operator in a magnetic field
............412
10.1.4
Helicity
eigenfunctions
.............................412
10.1.5
Eigenstates of the magnetic-moment operator
.........414
10.1.6
Eigenstates of the electric-moment operator
...........415
10.2
Spin-dependent electron gas
..............................416
10.2.1
Vertex function for
helicity
eigenstates
...............416
10.2.2
Vertex function for magnetic-moment eigenstates
......416
10.2.3
General properties of the vertex function
.............417
10.2.4
Spin dependence in Cerenkov emission
...............417
10.2.5
Spin dependent form of
П^{к)
.....................418
10.2.6
Separation of spin-dependent part
...................420
10.2.7
Response of an
isotropie
polarized electron gas
........421
10.3
Response tensor for bosonic plasmas
.......................422
10.3.1
Response tensor for a spin
0
gas
.....................422
10.3.2
Spin
1
plasmas
....................................424
10.3.3
Comparison of responses for spins
0, 5, 1.............424
10.3.4
Isotropie
degenerate
Bose
gases
.....................425
10.3.5
Dispersion relations in the degenerate limit
...........426
10.3.6
Pair and roton-like modes
..........................428
10.3.7
Dispersive properties of roton-like modes
.............429
10.4
Macroscopic mass renormalization
.........................430
10.4.1
Statistical average of the self energy
.................430
10.4.2
MMR in an
isotropie
medium
.......................430
10.4.3
Three different contributions to MMR
...............431
10.4.4
Form of
DßU(k) -
D™f{k) in an
isotropie
medium
.....432
10.4.5
Classical MMR
....................................433
10.4.6
MMR and the electromagnetic mass
.................434
10.4.7
Quasi-particles in an electron gas
....................434
10.4.8
Mass correction in the presence of waves
.............437
10.4.9
Ponderomotive force
...............................438
10.5
Properties of neutrinos in a plasma
........................439
10.5.1
Weak interactions and the electroweak theory
.........439
10.5.2
Interaction terms in the electroweak theory
...........440
10.5.3
Electron-neutrino scattering
........................441
10.5.4
Fierz transformation
...............................441
- :-f^no,,trmns
.......442
10.5.5
Macroscopic mass
renormalization for neutrinos
10.5.6
Neutrino MMR in an
isotropie
electron gas
...........444
10.6
Response of a neutrino gas
...............................446
10.6.1
Neutrino-photon vertex function
....................446
10.6.2 nbßlJ{k)
for an
isotropie
electron gas
..................448
10.6.3
Induced charge on the neutrino
.....................449
10.6.4
Cerenkov emission by a neutrino
....................449
.........450
10.6.5
Response of a neutrino gas
.451
10.6.6
Instability due to a neutrino beam
...................
^v.·.
References
..................................................452
Units and physical quantities
.........................
A.I Physical and plasma constants
.......................
A.
2
Units and dimensional analysis
.......................
453
453
454
Index
......
.457
|
| adam_txt |
Contents
Preface
.
V
1
Response 4-tensors
. 1
1.1
4-tensor
notation
. 2
1.1.1
4-tensor
equations
. 2
1.1.2
Important
4-
vectors
.
З
1.1.3
Lorentz
transformations
. 4
1.1.4
Specific transformation matrices
. 5
1.2
Electromagnetic field
. 7
1.2.1
Maxwell's equations
. 7
1.2.2
Electric and magnetic field 4-vectors
. 8
1.2.3
Invariants of the electromagnetic field
. 9
1.2.4
Continuity equations
. 10
1.2.5
Gauge transformations
. 10
1.3
Fourier transforms
. 12
1.3.1
4-dimensional Fourier transform
. 12
1.3.2
Truncations and the Dirac ¿-functions
. 13
1.3.3
Fourier transforms of the step and sign functions
. 14
1.3.4
Plemelj formula
. 15
1.3.5
Confinement to the forward light cone
. 15
1.4
Linear and nonlinear response 4-tensors
. 17
1.4.1
Induced current
. 17
1.4.2
Weak-turbulence expansion
. 17
1.4.3
Reality condition
. 18
1.4.4
Charge-continuity and gauge-invariance
. 18
1.4.5
Separation into dissipative and nondissipative parts
. 19
1.4.6
Kramers-Kronig relations
. 19
1.4.7
Onsager relations
. 20
1.4.8
Nonlinear response tensors
. 21
1.5
Alternative descriptions of the linear response
. 24
1.5.1
Alternative form of Maxwell's equations
. 24
χ
Contents
1.5.2
Response 3-tensors
for the
static response
. 24
1.5.3
Covariant
form for the
static response
. 25
1.5.4
Generalizations of phenomenological electrodynamics
. 26
1.5.5
Alternative form for the linear response
. 27
1.5.6
Conductivity 4-tensor
. 28
1.5.7
Response 3-tensors for plasmas
. 28
1.5.8
Construction of the 4-tensor from the 3-tensor
. 29
1.6 Isotropie
media
. 30
1.6.1
Covariant description of an
isotropie
medium
. 30
1.6.2
Construction of L^(k,u),T^{k,u), R»u{k,u)
. 31
1.6.3
Construction of nL(k),
Пт{к), Пн{к).
32
1.6.4
Static limit for an
isotropie
plasma
. 33
1.7
Response tensors for simple media
. 34
1.7.1
Cold unmagnetized plasma
. 34
1.7.2
Isotropie
dielectrics
. 35
1.7.3
Isotropie nonrelativistic
thermal plasma
. 35
References
. 36
2
Covariant theory of wave dispersion
. 37
2.1
Wave equation and the photon propagator
. 38
2.1.1
Wave equation
. 38
2.1.2
Homogeneous wave equation
. 38
2.1.3
Photon propagator
. 39
2.1.4
Formal construction of the propagator
. 39
2.1.5
Temporal gauge
. 41
2.1.6 Lorenz
gauge
. 41
2.1.7
Photon propagator in
vacuo
. 42
2.2
Evaluation of \(k) and X^aT(k)
. 43
2.2.1
Arbitrary
4x4
matrices
. 43
2.2.2
Cayley-Hamilton theorem
. 44
2.2.3
Traces of
Аџџ
. 45
2.2.4
Dispersion equation in terms of 3-tensor components
. 46
2.2.5
Relation between 3-tensor and 4-tensor formalisms
. 47
2.3
Dispersion relations and polarization 4-vectors
. 48
2.3.1
Dispersion equation
. 48
2.3.2
Inclusion of weak dissipation
. 49
2.3.3
Antihermitian part of the photon propagator
. 49
2.3.4
Polarization 4-vectors
. 50
2.3.5
Normalization of polarization 4-vectors
. 51
2.3.6
Ratio of electric to total energy
. 51
2.3.7
Alternative forms for R^j(k)
. 52
2.4
Wave damping and wave energetics
. 54
2.4.1
Wave amplitude and wave energy
. 54
2.4.2
Electromagnetic contributions to the wave energy
. 55
2.4.3
Wave action
. 55
2.4.4
Work done by the dissipative part
of the linear response
.
2 4 5
Absorption coefficient
.
2І4.6
Continuity equation for wave energy^
56
57
57
58
2.4.7
Interpretation of the energy-momentum tensor
.
uo
2.5
Waves in
isotropie
and weakly anisotropic media
. 59
2.5.1
Longitudinal and transverse waves
. 59
2.5.2
Polarization 4-vector for longitudinal waves
. 60
2.5.3
Transverse waves in optically active media
. 60
2.5.4
Degenerate transverse wave modes
. 61
2.5.5
Polarization of transverse waves
. 62
2.5.6
Sum over transverse states of polarization
. 63
2.5.7
Transverse waves in weakly anisotropic media
. 64
2.5.8
Transfer equation for polarized radiation
. 65
2.5.9
Stokes parameters
. 67
2.6
Lorentz
transformation of wave properties
. 69
2.6.1
Transformation of the wave 4-vector
. 69
2.6.2
Longitudinal waves in a nonrelativistic
thermal plasma
. 70
2.6.3
Langmuir waves in a moving frame
. 71
2.6.4
Transverse waves in a moving frame
. 72
2.6.5
Transformation of wave energetics
. 73
2.6.6
Transformation of Rm
. 74
References
. 75
3
Particle and wave subsystems
. 77
3.1
Covariant Lagrangians for free particles and fields
. 78
3.1.1
Lagrangian density
. 78
3.1.2
Orbit of the particle
. 79
3.1.3
Perturbation expansion in A{k)
. 80
3.1.4
Lagrangian density for a particle system
. 80
3.1.5
Euler-Lagrange equations for a field
. 81
3.1.6
Lagrangian density for the electromagnetic field
. 82
3.2
Background and wave subsystems
. 83
3.2.1
Forward-scattering approach
. 83
3.2.2
Vlasov
approach
. 83
3.2.3
Expansion about oscillation-center coordinates
. 84
3.2.4
Expansion of the Lagrangian
. 85
3.2.5
Second-order Lagrangian in fc-space
. 86
3.2.6
Nonlinear Lagrangian
. 87
3.2.7
Ponderomotive force
. 88
3.3
Forward-scattering method
. 90
3.3.1
Single particle current
. 90
3.3.2
Perturbation expansion for an unmagnetized plasma
. 90
3.3.3
Forward-scattering assumption
. 92
ЛИ
Contents
3.4
Cold plasma model
. 93
3.4.1
Covariant fluid equations
. 93
3.4.2
Perturbation expansion of the fluid equations
. 93
3.4.3
First and second order currents
. 95
3.4.4
Response tensors for a cold unmagnetized plasma
. 95
3.5
Covariant
Vlasov
theory
. 97
3.5.1
Statistical theory of plasmas
. 97
3.5.2
Boltzmann equation
. 98
3.5.3
Boltzmann equation in 8-dimensional phase space
. 99
3.5.4
Fluctuations in a plasma
.100
3.5.5
Two-scale separation of the distribution function
.101
3.5.6
Fluctuations for undressed particles
.102
3.5.7
Fluctuations in the current
.102
3.5.8
Fluctuations in the electromagnetic field
.103
3.6
Lagrangian description of a wave subsystem
.104
3.6.1
Lagrangian density a wave subsystem
.104
3.6.2
Euler-Lagrange equations for a wave subsystem
.105
3.6.3
Energy-momentum tensor Tfif{k)
.105
3.6.4
Inclusion of emission and absorption
.106
3.6.5
Lorentz
transformation of Tj^(fc)
.106
3.6.6
Energy-momentum tensor for static fields
.106
3.7
Covariant theory of ray propagation
.108
3.7.1
Wave Hamiltonian
.108
3.7.2
Eikonal approach
.109
3.7.3
Illustrative example: transverse waves
.110
3.7.4
Curved space-time
.110
3.7.5
Ray equations in curved space-time
.
Ill
3.7.6
Cold plasma in
a
Schwarzschild
metric
.112
3.7.7
Rays in a rotating coordinate frame
.113
References
.115
4
Dispersion in relativistic plasmas
.117
4.1
Linear response for an
isotropie
plasma
.118
4.1.1
General expressions for the linear response tensor
.118
4.1.2
Antihermitian part
.118
4.1.3
Number densities and plasma frequencies
.119
4.1.4
Response for an
isotropie
plasma
.120
4.1.5
Vlasov
form for an
isotropie
plasma
.122
4.2
Relativistic thermal distribution
.123
4.2.1
Jiittner distribution
.123
4.2.2
Properties of Kv{x)
.124
4.2.3
Average quantities
.125
4.3
Linear response of a relativistic thermal plasma
.127
4.3.1
Relativistic plasma dispersion function T{z,p)
.127
4.3.2
Derivation by the forward-scattering method
.127
Contents
лій
4.3.3
Derivation by the
Vlasov
approach
.128
4.3.4
SLlin's
method
.-.129
4.3.5
Trubnikov's integral
.130
4.3.6
Longitudinal and transverse parts
.133
4.4
Relativistic plasma dispersion functions (RPDPs)
.135
4.4.1
Definitions of plasma dispersion functions
.135
4.4.2
Real and imaginary parts of Trubnikov functions
.135
4.4.3
Properties of
Т(г,
p)
and
T'(z, p)
.138
4.4.4
Longitundinal
and transverse response functions
.140
4.4.5
Expansion for
z2 <
1.141
4.4.6
Expansion for z2
> 1.142
4.4.7
Weakly relativistic limit
.143
4.4.8
Nonrelativistic limit
.143
4.4.9
Ultrarelativistic limit
.144
4.4.10
Generalized Trubnikov functions
.144
4.5
Waves in relativistic thermal plasmas
.147
4.5.1
General dispersion relations
.147
4.5.2
Debye length
.147
4.5.3
Cutoff frequencies for
г2
» 1 .148
4.5.4
Dispersion curves for Langmuir waves
.149
4.5.5
Approximate dispersion relations for Langmuir waves
. 150
4.5.6
Landau damping
.151
4.5.7
Transverse waves
.152
4.5.8
Acoustic waves
.153
4.6
Instability due to anisotropic distributions
.155
4.6.1
Classes of anisotropic distributions
.155
4.6.2
Distributions with relative streaming
.156
4.6.3
Strictly-parallel thermal distribution
.156
4.6.4
Trubnikov's method for strictly-parallel distribution
. . 158
4.6.5
Strictly-perpendicular thermal distribution
.159
4.7
Nonlinear response tensors
.162
4.7.1
General forms for the nonlinear response tensors
.162
4.7.2
Alternative forms derived using the
Vlasov
approach
. 162
4.7.3
Linear response for a longitudinal slow disturbance
. 163
4.7.4
Nonlinear responses with one slow disturbance
.164
4.7.5
Electrostatic model
.165
4.7.6
Two fast and two slow disturbances
.166
References
.167
5
Classical plasmadynamics
.169
5.1
Spontaneous emission
.170
5.1.1
Radiation field
.170
5.1.2 4-
momentum radiated
.171
5.1.3
Probability of emission
.172
5.1.4
Probability for Cerenkov emission
.172
XIV Contents
5.1.5
Cerenkov
condition
.173
5.1.6
Quantum
recoil
.174
5.2 Quasilinear
equations
.175
5.2.1
Detailed balance
.175
5.2.2
Transfer equation for waves
.175
5.2.3 Quasilinear
equation for particles
.177
5.2.4
Conservation of 4-momentum
.178
5.2.5
Interpretation of the
quasilinear
diffusion coefficients
. 179
5.2.6
Radiation reaction force
.179
5.2.7
Quantum recoil in spontaneous emission
.180
5.2.8
Covariant Fokker-Planck equation
.181
5.2.9
Second Fokker-Planck coefficient
.181
5.2.10
First Fokker-Planck coefficient
.182
5.3
Specific emission processes
.184
5.3.1
Power radiated in Cerenkov emission
.184
5.3.2
Appearance emission
.185
5.3.3
Transition radiation
.186
5.3.4
Electron-ion collisions
.186
5.3.5
Bremsstrahlung: the impulsive model
.187
5.3.6
Bremsstrahlung: the straight line approximation
.189
5.4
Fluctuations and the collision integral
.192
5.4.1
Form of the collision integral
.192
5.4.2
Kinetic equation due to fluctuations
.193
5.4.3
Inclusion of the self-consistent field
.193
5.4.4 Quasilinear
equation
.194
5.4.5
Collision integral
.195
5.4.6
Fluctuations in an
isotropie
plasma
.196
5.4.7
Scattering probability in an
isotropie
plasma
.196
5.4.8
Collisions involving nonrelativistic particles
.197
5.4.9
Electron-electron collisions in a relativistic plasma
.198
5.5
Scattering of waves by particles
.200
5.5.1
Current associated with scattering
.200
5.5.2
Probability for scattering
.201
5.5.3
Kinetic equations for scattering
.202
5.5.4
Double emission and double absorption
.204
5.5.5
Interference between Thomson and nonlinear
scattering
.205
5.5.6
Virtual longitudinal and transverse waves
.206
5.6
Thomson and inverse Compton scattering
.207
5.6.1
Thomson scattering in
vacuo
.207
5.6.2
Scattering of an
isotropie
distribution of photons
.208
5.6.3
Scattering kernel
.209
5.6.4
Exact results for Thomson scattering
.211
5.6.5
Kinetic equation for
isotropie
particles and photons
. 212
5.6.6
Kompaneets equation
.212
Contents XV
5.6.7
Inverse Compton scattering
.214
5.6.8
Induced scattering by relativistic electrons
.215
5.7
Wave-wave interactions
.217
5.7.1
Three-wave interactions
.217
5.7.2
Probability for a three-wave interaction
.217
5.7.3
Kinetic equations for three-wave processes
.219
5.7.4
Current for four-wave interactions
.219
5.7.5
Effective cubic response
.221
5.7.6
Four-wave interactions
.221
5.7.7
Kinetic equations for three-wave coalescence
.222
5.7.8
Kinetic equations for wave-wave scattering
.223
5.7.9
Phase-coherent interactions
.223
5.8
Nonlinear wave equations
.226
5.8.1
Nonlinear correction to the linear response
.226
5.8.2
Nonlinear effects involving two different wave modes
. 226
5.8.3
Nonlinear damping processes
.227
5.8.4
Nonlinearity involving a single wave mode
.229
5.8.5
Zakharov equations
.230
References
.232
6
Quantum field theory
.233
6.1
Relativistic wave equations
.234
6.1.1
State functions and operators in a Hilbert space
.234
6.1.2
Link between classical and quantum descriptions
.235
6.1.3
Pictures of the time evolution
.235
6.1.4
Representations
.236
6.1.5
Klein-Gordon equation
.237
6.1.6
Dirac equation
.238
6.1.7
Covariant form of Dirac's equation
.238
6.1.8
Dirac Hamiltonian
.239
6.1.9
Standard representation
.240
6.1.10
Dirac matrices
σμι>
and 75
.241
6.1.11
Basic set of Dirac matrices
.241
6.1.12
Traces of products of 7-matrices
.242
6.2
Wavefunctions for relativistic particles
.243
6.2.1
Generic solutions
.243
6.2.2
Plane wavefunctions
.244
6.2.3
Solutions in the standard representation
.245
6.2.4
Orthogonality and completeness relations
.245
6.2.5
Wavefunctions us(p), va(p)
.246
6.2.6
Neutrinos
.246
6.3
Lagrangian formulation
.248
6.3.1
Klein-Gordon Lagrangian
.248
6.3.2
Dirac Lagrangian
.248
6.3.3
Particle action and occupation numbers
.249
6.3.4
Inclusion
of an electromagnetic field
.250
6.3.5
Magnetic moment of the electron
.251
6.3.6
Interaction between Dirac and EM fields
.251
6.3.7
Interaction between Klein-Gordon and EM fields
.252
6.4
Second quantization
.253
6.4.1
Harmonic oscillator
.253
6.4.2
Quantization of fields
.254
6.4.3
Anticommutation relations
for fermion fields
.255
6.4.4
Quantization of fermion fields
.256
6.4.5
Normal ordering
.257
6.5
Propagators
.258
6.5.1
Solution of inhomogeneous wave equation
.258
6.5.2
Feynman contour
.259
6.5.3
Chronological operator
.260
6.5.4
Vacuum expectation value
.260
6.5.5
Electron propagator as a vacuum expectation value
. 261
6.5.6
Contractions
.262
6.5.7
Boson propagator
.262
6.5.8
Photon propagator as a vacuum expectation value
.263
6.6
Scattering matrix (5-matrix)
.264
6.6.1
Interaction picture
.264
6.6.2
Evolution of
Š
.265
6.6.3
Interaction Hamiltonian in QED
.265
6.6.4
Initial and final states
.266
6.6.5
Scattering amplitudes
7}¡
and Ma
.266
6.6.6
Additional interaction terms
.267
6.6.7
Nonlinear responses in QPD
.268
6.6.8
Interaction Hamiltonian in
SED.269
6.7
Elements in Feynman diagrams
.270
6.7.1
Connected and disjoint diagrams
.270
6.7.2
First order diagrams in QED
.271
6.7.3
Crossed diagrams
.273
6.7.4
Multiple-photon vertices
.273
6.7.5
Second-order processes
.274
6.7.6
Propagators
.275
6.7.7
Loop momentum
.275
6.7.8
External fields
.276
6.7.9
Vertex formalism
.276
6.7.10
Momentum-space representation
.277
References
.278
7
QPD processes
.279
7.1
Rules for Feynman diagrams
. 280
7.1.1
Rules for drawing diagrams
.280
7.1.2
Rules for constructing
Sa
.281
7.1.3
Rules for momentum space representations
.282
7.1.4
Rules for the vertex formalism and for
SED.283
7.1.5
Rules for weak interactions
.284
7.2
First-order processes
.286
7.2.1
Conservation of 4-momentum
.286
7.2.2
Transition rate for Cerenkov emission
.286
7.2.3
Probability of Cerenkov emission
.288
7.2.4
Cerenkov emission by an unpolarized electron
.289
7.2.5
Kinetic equations for Cerenkov emission
.290
7.2.6
Kinetic equation for the particles
.291
7.2.7
Power radiated in transverse waves
.291
7.2.8
One-photon pair creation
.292
7.2.9
Kinetic equations for one-photon pair creation
.292
7.3
Scattering processes
. 294
7.3.1
Invariant kinematics
.294
7.3.2
Mandelstam
diagram
.296
7.3.3
Scattering cross section
.296
7.3.4
Application to Compton scattering
.299
7.4
Compton scattering and related processes
.300
7.4.1
Compton scattering and nonlinear scattering
.300
7.4.2
Derivation using the vertex formalism
.301
7.4.3
Probability for Compton scattering
.302
7.4.4
Kinetic equations for Compton scattering
.302
7.4.5
Compton scattering in
vacuo
.303
7.4.6
Corrections for Compton scattering in a plasma
.304
7.4.7
Compton scattering of unpolarized photons
.305
7.4.8
Compton cross section
.305
7.4.9
Klein-Nishina cross section
.306
7.5
Mot-t scattering and bremsstrahlung
.308
7.5.1
Scattering of an electron by a Coulomb field
.308
7.5.2
Mott
scattering
.308
7.5.3
Mott
cross section
.309
7.5.4
Bremsstrahlung in
Mott
scattering
.310
7.5.5
Bremsstrahlung emission of soft photons
.311
7.6
Electron-electron scattering
.314
7.6.1
Probability for M0ller scattering
.314
7.6.2
Dependence on momentum transfer
.315
7.6.3
Kinetic equation for M0ller scattering
.316
7.6.4
M0ller scattering
in vacuo
.316
7.6.5
Bhabha scattering
.318
7.6.6
Small-angle M0ller scattering in a plasma
.319
7.6.7
Scattering in relativistic degenerate plasma
.320
References
.321
Responses of a quantum plasma
.323
8.1
Renormalization and regularization
.324
8.1.1
Divergent diagrams
.324
8.1.2
Vacuum polarization
.324
8.1.3
Regularization of the vacuum polarization tensor
.326
8.1.4
Effect of the vacuum polarization
on a Coulomb field
.328
8.1.5
Cubic response tensor for the vacuum
.328
8.1.6
Dimensional restrictions on higher order responses
.330
8.1.7
Mass operator
.331
8.1.8
Vertex correction and the Ward identity
.332
8.2
Statistical average over a plasma
.334
8.2.1
Density matrix
.334
8.2.2
Statistical averages
.334
8.2.3
Statistically averaged propagators
.335
8.2.4
Spin dependence of the averaged propagator
.336
8.2.5
Statistically averaged photon propagator
.337
8.2.6
Forward scattering and cuts in closed loops
.337
8.2.7
Unitarity
.338
8.2.8
Linear and nonlinear responses
.339
8.2.9
Macrosocpic mass renormalization
.340
8.3
General forms for linear response tensor
.341
8.3.1
Linear response tensor
.341
8.3.2
Alternative forms for
Пџџ{к)
.341
8.3.3
Electron and positron contributions
.342
8.3.4
Charge-symmetric form
.343
8.3.5
Antihermitian part of the response tensor
.343
8.3.6
Resonance conditions
.344
8.3.7
Quantum recoil
.345
8.3.8
Solutions of the resonance conditions
.346
8.3.9
Allowed resonances
.347
8.4
Wigner matrix and density matrix approaches
.349
8.4.1
Quasi-probability distribution
.349
8.4.2
Covariant Wigner matrix
.350
8.4.3
Basis set of covariant Wigner functions
.351
8.4.4
First order Wigner functions
.352
8.4.5
Linear response tensor from the Wigner matrix
.352
8.4.6
Fluctuations in a quantum plasma
.353
8.4.7
Fluctuations in the Wigner matrix
.354
8.4.8
Fluctuations in the 4-current
.355
8.4.9
Kubo's formula
.355
8.4.10
Density matrix approach
.356
8.4.11
Expansion of the density matrix
.357
8.4.12
Linear response tensor
.357
8.5
Nonlinear response tensors
.359
8.5.1
Closed particle loops
.359
8.5.2
nth order nonlinear response tensor
.359
8.5.3
Quadratic response tensor for an electron gas
.360
8.5.4
Cubic response tensor for an electron gas
.361
8.6
Inclusion of a photon gas
.363
8.6.1
Linear response due to a photon gas
.363
8.6.2
Relation to three-wave coupling
.365
8.6.3
Instability due to a photon beam
.365
8.6.4
Nonlinear effects of a photon gas
.366
8.6.5
Dissipation modified by a photon gas
.367
8.6.6
Turbulent bremsstrahlung
.368
References
.369
9
Isotropie
quantum plasmas
.371
9.1
Isotropie
distributions
.372
9.1.1
Separation into longitudinal and transverse parts
.372
9.1.2
Isotropie
distribution in its rest frame
.373
9.1.3
Tsytovich's form for
Пь'т{к)
.374
9.1.4
Integral over angles
.375
9.1.5
Relativistic quantum dispersion functions
.376
9.1.6
Nonquantum limit
. 377
9.1.7
Fermi-Dirac distribution
.377
9.2
Dissipation in
isotropie
quantum plasmas
.378
9.2.1
Boundary of the resonance regions
.378
9.2.2
Alternative forms of
Λχ
,
Л2.
379
9.2.3
Imaginary parts of the plasma dispersion functions
. 379
9.2.4
Imaginary parts of the tfL(fc),
Пт(к).
381
9.3
Linear response of a degenerate plasma
.382
9.3.1
Degenerate limit
.382
9.3.2
Evaluation of specific integrals
.383
9.3.3
RQPDFs in the completely degenerate limit
.384
9.3.4
Jancovici's response functions
.385
9.3.5
Dissipation due to LD and PC
.386
9.3.6
Neglect of the quantum recoil
.387
9.3.7
Lindhard's response tensor
.388
9.4
Linear response of
a nondegenerate
plasma
.390
9.4.1
Nondegenerate
limit
.390
9.4.2
Dispersion functions in the nondegenerate limit
.391
9.4.3
Evaluation in terms of T{v, p)
.391
9.4.4
Dispersion functions for nondegenerate plasma
.392
9.4.5
Nonquantum limit
.393
9.4.6
Lowest order quantum corrections
.393
9.4.7
High temperature limit
.394
9.4.8
Nearly
nondegenerate
limit
.394
9.5
Dispersion in
isotropie
plasmas
.396
9.5.1
Debye-like screening
.396
9.5.2
Friedel oscillations in relativistic degenerate plasmas
. 396
9.5.3
Magnetic susceptibility of an electron gas
.398
9.5.4
Cutoff frequency
.398
9.5.5
Waves in
nondegenerate
thermal plasmas
.400
9.6
Waves in completely degenerate electron gas
.402
9.6.1
Langmuir waves in degenerate electron gas
.402
9.6.2
Longitudinal response function
.403
9.6.3
Longitudinal waves including relativistic effects
.406
9.6.4
Superdense
plasmas
.407
References
.408
10
Spin, MMR and neutrino plasma
.409
10.1
Spin operators and eigenfunctions
.410
10.1.1
Conserved quantities and constants of the motion
.410
10.1.2
Spin operators
.411
10.1.3
Preferred spin operator in a magnetic field
.412
10.1.4
Helicity
eigenfunctions
.412
10.1.5
Eigenstates of the magnetic-moment operator
.414
10.1.6
Eigenstates of the electric-moment operator
.415
10.2
Spin-dependent electron gas
.416
10.2.1
Vertex function for
helicity
eigenstates
.416
10.2.2
Vertex function for magnetic-moment eigenstates
.416
10.2.3
General properties of the vertex function
.417
10.2.4
Spin dependence in Cerenkov emission
.417
10.2.5
Spin dependent form of
П^{к)
.418
10.2.6
Separation of spin-dependent part
.420
10.2.7
Response of an
isotropie
polarized electron gas
.421
10.3
Response tensor for bosonic plasmas
.422
10.3.1
Response tensor for a spin
0
gas
.422
10.3.2
Spin
1
plasmas
.424
10.3.3
Comparison of responses for spins
0, 5, 1.424
10.3.4
Isotropie
degenerate
Bose
gases
.425
10.3.5
Dispersion relations in the degenerate limit
.426
10.3.6
Pair and roton-like modes
.428
10.3.7
Dispersive properties of roton-like modes
.429
10.4
Macroscopic mass renormalization
.430
10.4.1
Statistical average of the self energy
.430
10.4.2
MMR in an
isotropie
medium
.430
10.4.3
Three different contributions to MMR
.431
10.4.4
Form of
DßU(k) -
D™f{k) in an
isotropie
medium
.432
10.4.5
Classical MMR
.433
10.4.6
MMR and the electromagnetic mass
.434
10.4.7
Quasi-particles in an electron gas
.434
10.4.8
Mass correction in the presence of waves
.437
10.4.9
Ponderomotive force
.438
10.5
Properties of neutrinos in a plasma
.439
10.5.1
Weak interactions and the electroweak theory
.439
10.5.2
Interaction terms in the electroweak theory
.440
10.5.3
Electron-neutrino scattering
.441
10.5.4
Fierz transformation
.441
"
-':-f^no,,trmns
.442
10.5.5
Macroscopic mass
renormalization for neutrinos
10.5.6
Neutrino MMR in an
isotropie
electron gas
.444
10.6
Response of a neutrino gas
.446
10.6.1
Neutrino-photon vertex function
.446
10.6.2 nbßlJ{k)
for an
isotropie
electron gas
.448
10.6.3
Induced charge on the neutrino
.449
10.6.4
Cerenkov emission by a neutrino
.449
.450
10.6.5
Response of a neutrino gas
.451
10.6.6
Instability due to a neutrino beam
.
^v.·.
References
.452
Units and physical quantities
.
A.I Physical and plasma constants
.
A.
2
Units and dimensional analysis
.
453
453
454
Index
.
.457 |
| any_adam_object | 1 |
| any_adam_object_boolean | 1 |
| author | Melrose, Donald B. 1940- |
| author_GND | (DE-588)172255007 |
| author_facet | Melrose, Donald B. 1940- |
| author_role | aut |
| author_sort | Melrose, Donald B. 1940- |
| author_variant | d b m db dbm |
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| bvnumber | BV023092612 |
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| discipline | Physik |
| discipline_str_mv | Physik |
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| id | DE-604.BV023092612 |
| illustrated | Not Illustrated |
| index_date | 2024-07-02T19:41:38Z |
| indexdate | 2024-07-09T21:10:50Z |
| institution | BVB |
| isbn | 9780387739021 9780387739038 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-016295461 |
| oclc_num | 634512242 |
| open_access_boolean | |
| owner | DE-384 DE-11 DE-703 |
| owner_facet | DE-384 DE-11 DE-703 |
| physical | XXI, 464 S. graph. Darst. |
| publishDate | 2008 |
| publishDateSearch | 2008 |
| publishDateSort | 2008 |
| publisher | Springer |
| record_format | marc |
| series | Lecture notes in physics |
| series2 | Lecture notes in physics |
| spelling | Melrose, Donald B. 1940- Verfasser (DE-588)172255007 aut Quantum plasmadynamics unmagnetized plasmas Donald B. Melrose New York, NY Springer 2008 XXI, 464 S. graph. Darst. Lecture notes in physics 735 Quantenelektrodynamik (DE-588)4047982-1 gnd rswk-swf Plasmadynamik (DE-588)4123952-0 gnd rswk-swf Quantenelektrodynamik (DE-588)4047982-1 s Plasmadynamik (DE-588)4123952-0 s DE-604 Lecture notes in physics 735 (DE-604)BV000003166 735 Digitalisierung UB Augsburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016295461&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Melrose, Donald B. 1940- Quantum plasmadynamics unmagnetized plasmas Lecture notes in physics Quantenelektrodynamik (DE-588)4047982-1 gnd Plasmadynamik (DE-588)4123952-0 gnd |
| subject_GND | (DE-588)4047982-1 (DE-588)4123952-0 |
| title | Quantum plasmadynamics unmagnetized plasmas |
| title_auth | Quantum plasmadynamics unmagnetized plasmas |
| title_exact_search | Quantum plasmadynamics unmagnetized plasmas |
| title_exact_search_txtP | Quantum plasmadynamics unmagnetized plasmas |
| title_full | Quantum plasmadynamics unmagnetized plasmas Donald B. Melrose |
| title_fullStr | Quantum plasmadynamics unmagnetized plasmas Donald B. Melrose |
| title_full_unstemmed | Quantum plasmadynamics unmagnetized plasmas Donald B. Melrose |
| title_short | Quantum plasmadynamics |
| title_sort | quantum plasmadynamics unmagnetized plasmas |
| title_sub | unmagnetized plasmas |
| topic | Quantenelektrodynamik (DE-588)4047982-1 gnd Plasmadynamik (DE-588)4123952-0 gnd |
| topic_facet | Quantenelektrodynamik Plasmadynamik |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016295461&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000003166 |
| work_keys_str_mv | AT melrosedonaldb quantumplasmadynamicsunmagnetizedplasmas |