Quantum theory of near-field electrodynamics:
Gespeichert in:
| 1. Verfasser: | |
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| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Berlin [u.a.]
Springer
2011
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| Schriftenreihe: | Nano-optics and nanophotonics
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| Schlagworte: | |
| Online-Zugang: | Inhaltstext Inhaltsverzeichnis |
| Beschreibung: | XXV, 667 S. graph. Darst. |
| ISBN: | 9783642174094 3642174094 9783642174100 |
Internformat
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| 245 | 1 | 0 | |a Quantum theory of near-field electrodynamics |c Ole Keller |
| 264 | 1 | |a Berlin [u.a.] |b Springer |c 2011 | |
| 300 | |a XXV, 667 S. |b graph. Darst. | ||
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Datensatz im Suchindex
| _version_ | 1805145437423796224 |
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IMAGE 1
CONTENTS
PART I MICROSCOPIC CLASSICAL THEORY 1 SURVEY OF THE CLASSICAL THEORY 3
1.1 WHY IS THE CLASSICAL THEORY NEEDED? 3
1.2 CLASSICAL ELECTRODYNAMICS: MACROSCOPIC VS. MICROSCOPIC THEORY 4
1.3 MAXWELL-LORENTZ ELECTRODYNAMICS 6
1.4 THE STANDARD GREEN FUNCTIONS (NOT PROPAGATORS) 7
1.5 EVANESCENT ELECTROMAGNETIC FIELDS 8
1.6 MULTIPOLE ELECTRODYNAMICS: A RICHLY FACETED SUBJECT 11 1.7 LOCAL
ELECTROMAGNETIC FIELDS AND RESONANCES 14
1.8 RADIATION REACTION IN A CLASSICAL PERSPECTIVE 15
2 MAXWELL-LORENTZ ELECTRODYNAMICS IN SPACE-TIME 17
2.1 THE MAXWELL-LORENTZ EQUATIONS 17
2.2 VECTOR AND SCALAR POTENTIALS: GAUGE INVARIANCE 17
2.3 THE IMPLICIT SOLUTION OF THE MAXWELL-LORENTZ EQUATIONS 19 2.4 THE
NEWTON-LORENTZ EQUATION 22
2.5 THE LIENARD-WIECHERT POTENTIALS AND FIELDS 23
2.6 SOME IMPORTANT GLOBAL CONSERVATION LAWS 28
2.6.1 GLOBAL ENERGY CONSERVATION 28
2.6.2 GLOBAL MOMENTUM CONSERVATION 30
2.6.3 GLOBAL ANGULAR MOMENTUM CONSERVATION 32
2.7 SOME LOCAL CONSERVATION LAWS 33
2.7.1 CHARGE CONSERVATION 33
2.7.2 LOCAL ENERGY CONSERVATION: MICROSCOPIC POYNTING VECTOR 34
2.7.3 LOCAL MOMENTUM CONSERVATION: MAXWELL STRESS TENSOR 35
2.7.4 LOCAL ANGULAR MOMENTUM CONSERVATION: ANGULAR MOMENTUM FLOW 37
BIBLIOGRAFISCHE INFORMATIONEN HTTP://D-NB.INFO/100790416X
DIGITALISIERT DURCH
IMAGE 2
XII CONTENTS
3 ELECTROMAGNETIC GREEN FUNCTIONS IN SPECTRAL REPRESENTATION 39 3.1 THE
MAXWELL-LORENTZ EQUATIONS IN THE SPACE-FREQUENCY DOMAIN 39
3.2 DYADIC GREEN FUNCTIONS IN THE SPACE-FREQUENCY DOMAIN 40 3.2.1 GREEN
FUNCTION FOR THE ELECTRIC FIELD 40
3.2.2 GREEN FUNCTION FOR THE MAGNETIC FIELD 42
3.3 NEAR-, MID-, AND FAR-FIELD PARTS OF G AND G M 43
3.3.1 GREEN FUNCTIONS IN SPHERICAL COORDINATES 43
3.3.2 FAR-FIELD ZONE 44
3.3.3 MID-FIELD TERMS 45
3.3.4 NEAR-FIELD ZONE 45
3.4 GREEN FUNCTIONS AND WAVE EQUATIONS IN THE SPACE-FREQUENCY DOMAIN 46
3.5 SPECTRAL REPRESENTATION OF THE ELECTROMAGNETIC FIELD FROM AN
ASSEMBLY OF MOVING POINT PARTICLES 48
4 ANGULAR SPECTRUM REPRESENTATION OF THE GREEN FUNCTIONS AND FIELDS 51
4.1 MAXWELL-LORENTZ EQUATIONS IN MIXED REPRESENTATION 51 4.2 INTERLUDE:
MONOCHROMATIC PLANE-WAVE REPRESENTATION OF THE MAXWELL-LORENTZ EQUATIONS
AND GREEN FUNCTIONS 53 4.3 GREEN FUNCTIONS IN MIXED REPRESENTATION 56
4.3.1 SCALAR PROPAGATOR, G(Z;Q^CO) 56
4.3.2 DYADIC GREEN FUNCTION, G(Z;Q§,CO) 58
4.3.3 DYADIC GREEN FUNCTION, G M (Z;Q^ , CO) 59
4.4 EVANESCENT ELECTROMAGNETIC FIELDS 60
4.4.1 ELECTROMAGNETIC FIELDS FROM A SHEET SOURCE 60
4.4.2 TRANSFER MATRICES 61
4.4.3 MIXED CURRENT DENSITY OF A MOVING POINT CHARGE 62 4.4.4
CYCLE-AVERAGED FIELD MOMENTUM DENSITY 63
4.5 NONRETARDED (CO - OO) ELECTRODYNAMICS IN VACUUM 66
4.6 WEYL REPRESENTATION OF THE GREEN FUNCTIONS 68
4.6.1 INTEGRALS OVER PROPAGATING AND EVANESCENT WAVES 68 4.6.2 INTEGRALS
OVER GENERALIZED INHOMOGENEOUS WAVES 71
5 MULTIPOLE ELECTRODYNAMICS 75
5.1 MOMENT EXPANSION OF LOCALIZED CURRENT DENSITY DISTRIBUTION 75 5.2
ELECTRIC AND MAGNETIC DIPOLE FIELDS 79
5.3 ELECTRIC QUADRUPOLE FIELDS 81
5.4 TRANSVERSE ELECTROMAGNETIC MULTIPOLE WAVES 83
5.4.1 SPHERICAL SCALAR WAVES 83
5.4.2 INTERLUDE: ANGULAR FIELD MOMENTUM OPERATOR J 85 5.4.3 ELECTRIC AND
MAGNETIC MULTIPOLE FIELDS 87
5.5 MICROSCOPIC SOURCES OF MULTIPOLE FIELDS 89
5.5.1 MICROSCOPIC MAXWELL EQUATIONS WITH A NEW ELECTRIC-FIELD VARIABLE
89
IMAGE 3
CONTENTS XIII
5.5.2 INTERLUDE: SPHERICAL WAVE EXPANSION OF THE HUYGENS PROPAGATOR 91
5.5.3 MULTIPOLE COEFFICIENTS 92
5.6 MESOSCOPIC PARTICLE IN A PRESCRIBED EXTERNAL ELECTROMAGNETIC FIELD
94
5.6.1 RATE OF ENERGY TRANSFER 94
5.6.2 RATE OF MOMENTUM TRANSFER 95
5.6.3 ANGULAR MOMENTUM TRANSFER 96
6 ELECTRODYNAMIC INTERACTION BETWEEN POINT DIPOLES: LOCAL FIELDS 99
6.1 MULTIPLE ED-SCATTERING TO INFINITE ORDER 99
6.2 ED-SCATTERING IN A BORN SERIES APPROACH 102
6.3 LOCAL-FIELD RESONANCES 105
6.4 TWO-PARTICLE INTERACTION 106
6.5 MULTIPLE MD- AND EQ-SCATTERING 108
7 RADIATION REACTION I LL
7.1 THE NONRELATIVISTIC ABRAHAM-LORENTZ EQUATION OF MOTION I LL 7.2
DAMPING FORCE ON ELECTRIC AND MAGNETIC DIPOLES 116
7.2.1 BARE AND DRESSED ELECTRIC-DIPOLE POLARIZABILITY 116 7.2.2
NEAR-ZONE ELECTRIC GREEN FUNCTION: RADIATION DAMPING 118
7.2.3 MAGNETIC RADIATION DAMPING 119
7.3 THE RELATIVISTIC LORENTZ-DIRAC EQUATION OF MOTION 120 7.3.1
MANIFESTLY COVARIANT EXPRESSION FOR THE ENERGY-MOMENTUM RADIATION RATE
120 7.3.2 REST-MASS PRESERVING INTERACTIONS 122
7.3.3 ABRAHAM FOUR-VECTOR OF RADIATION REACTION 124 7.3.4 LORENTZ-DIRAC
EQUATION ON INTEGRO-DIFFERENTIAL FORM 125
7.4 SELF-FIELD DISTORTIONS 126
PART II QUANTUM THEORY WITH CLASSICAL FIELDS
8 ABOUT LOCAL-FIELD THEORY BASED ON ELECTRON-PHOTON WAVE MECHANICS 131
8.1 DYNAMICAL VARIABLES AND REDUNDANCY: RIM ZONE 132
8.2 LINEAR RESPONSE THEORY IN A MICROSCOPIC PERSPECTIVE 133 8.3 ON THE
QUANTUM MECHANICAL CALCULATION OF MICROSCOPIC CONDUCTIVITY TENSORS 136
8.4 COUPLED-ANTENNA THEORY 137
8.5 ELECTROMAGNETIC PROPAGATORS AND NONRETARDED TRANSVERSE RESPONSE 138
IMAGE 4
XIV CONTENTS
8.6 PHOTON WAVE MECHANICS: A REINTERPRETATION OF MAXWELLS THEORY 139
8.7 NEAR-FIELD AND GAUGE PHOTONS: PHOTON EMBRYO 141
8.8 PHOTON SPIN AND HELICITY 142
8.9 SUPERLOCALIZATION: ONE-PARTICLE POSITION OPERATORS 143 8.10
TRANSVERSE PHOTON MASS: EIKONAL THEORY FOR PHOTONS 143
9 TRANSVERSE AND LONGITUDINAL ELECTRODYNAMICS 145
9.1 SOLENOIDAL AND IRROTATIONAL VECTOR FIELDS 145
9.1.1 HELMHOLTZ THEOREM 145
9.1.2 DECOMPOSITION IN RECIPROCAL SPACE 146
9.1.3 TRANSVERSE AND LONGITUDINAL DELTA-FUNCTION DYADICS 147 9.2
TRANSVERSE AND LONGITUDINAL PARTS OF THE MAXWELL-LORENTZ EQUATIONS 149
9.2.1 FIELD EQUATIONS IN DIRECT SPACE 149
9.2.2 RIM ZONE OF MATTER 151
9.2.3 FIELD EQUATIONS IN RECIPROCAL SPACE 152
9.2.4 POTENTIAL DESCRIPTION 152
9.3 ROLE OF THE LONGITUDINAL ELECTRIC FIELD 154
9.3.1 INSTANTANEOUS COULOMB FIELD 154
9.3.2 COULOMB INTERACTION AND SELF-ENERGY 155
9.3.3 PARTICLE MOMENTUM ASSOCIATED WITH THE LONGITUDINAL ELECTRIC FIELD
157
9.3.4 PARTICLE ANGULAR MOMENTUM ASSOCIATED WITH THE LONGITUDINAL
ELECTRIC FIELD 160
9.4 DYNAMICAL STATE OF THE COUPLED FIELD-PARTICLE SYSTEM 162
10 LINEAR NONLOCAL RESPONSE THEORY 163
10. 1 RESPONSE THEORY FOR TRANSVERSE EXTERNAL EXCITATIONS 163 10.1.1
MANY-BODY CONSTITUTIVE RELATION 163
10.1.2 INTEGRAL EQUATION FOR THE TRANSVERSE ELECTRIC FIELD 165
10.1.3 CAUSAL RESPONSE TENSORS: MICROSCOPIC CONDUCTIVITY 166 10.2
CAUSALITY AND DISPERSION RELATIONS 167
10.2.1 EINSTEIN CAUSALITY AND MICROCAUSALITY 167
10.2.2 CAUSALITY AND ANALYTICITY: TRANSLATIONAL INVARIANCE IN TIME 168
10.2.3 FREQUENCY DISPERSION AND HUBERT TRANSFORMS 170 10.3 LOCAL AND
NEAR-LOCAL MICROSCOPIC RESPONSE TENSORS 172 10.3.1 SPATIAL CORRELATION
RANGE IN CONSTITUTIVE EQUATIONS 172
10.3.2 LOCAL DYNAMICS WITH HIDDEN NONLOCALITY 174
10.4 MICROSCOPIC "POLARIZATION" AND "MAGNETIZATION" DYNAMICS 175 10.4.1
GENERALIZED POLARIZATION AND MAGNETIZATION CONCEPTS 175 10.4.2
GENERALIZED ELECTRIC DISPLACEMENT AND MAGNETIC VECTOR FIELDS 177
10.4.3 CENTRAL FIELD EQUATIONS 178
IMAGE 5
CONTENTS XV
10.5 RESPONSE THEORY BASED ON GENERALIZED PERMITTIVITY AND PERMEABILITY
TENSORS FOR TRANSVERSE DYNAMICS 179 10.5.1 FLEXIBILITY 179
10.5.2 RESPONSE THEORY BASED ON THE CHOICE FL T (R,R',T,T') =
U8(R-R')8(T-T') 180
10.5.3 RESPONSE THEORY BASED ON THE CHOICE D T (R, T) = EOFIFO-, 0 181
10.6 RESPONSE TO EXTERNAL LONGITUDINAL FIELDS 182
10.7 THE GENERAL CONSTITUTIVE RELATION 183
10.8 RESPONSE TENSORS FOR MEDIA WITH FINITE AND INFINITESIMAL
TRANSLATIONAL INVARIANCE IN SPACE 184 10.8.1 LATTICE PERIODICITY 184
10.8.2 SLOWLY VARYING EXTERNAL FIELDS 1 85
11 DENSITY MATRIX FORMALISM: HAMILTON AND CURRENT DENSITY OPERATORS -
GAUGE INVARIANCE 187
11.1 DENSITY MATRIX OPERATOR 187
11.1.1 PURE STATE 187
11.1.2 STATISTICAL MIXTURE OF STATES 190
11.2 THE LIOUVILLE EQUATION 193
11.3 THE CONFIGURATION SPACE REPRESENTATION 195
11.4 HAMILTON OPERATOR IN MINIMAL COUPLING FORM 197
11.4.1 THE RELATIVISTIC STANDARD HAMILTONIAN 197
11.4.2 PAULI AND NONRELATIVISTIC HAMILTONIANS 199
11.4.3 CANONICAL QUANTIZATION 200
11.5 ORBITAL PROBABILITY CURRENT DENSITY 204
11.5.1 PROBABILITY CURRENT DENSITY IN WAVE FUNCTION SPACE 204 11.5.2
PARA- AND DIAMAGNETIC CURRENT DENSITIES 205
11.5.3 TRANSITION CURRENT DENSITY 206
11.5.4 ORBITAL CURRENT DENSITY OPERATOR 207
11.6 GAUGE INVARIANCE IN QUANTUM MECHANICS 209
11.6.1 TRANSFORMATION OF THE MECHANICAL MOMENTUM OPERATOR. .209 11.6.2
UNITARY TRANSFORMATION OF THE STATE VECTOR 210 11.6.3 FORM INVARIANCE OF
THE SCHROEDINGER EQUATION 212 11.6.4 ELECTROMAGNETIC FORCES AND LOCAL
PHASE INVARIANCE 214
12 QUANTUM THEORY OF THE GENERALIZED NONLOCAL LINEAR RESPONSE 217
12.1 MEAN VALUE OF THE ORBITAL CURRENT DENSITY OPERATOR IN A WEAK
EXTERNAL ELECTROMAGNETIC FIELD 217
12.1.1 GAUGE CHOICES FOR THE EXTERNAL AND INDUCED POTENTIALS:
INTERACTION HAMILTONIAN 217
12.1.2 ITERATIVE SOLUTION OF THE LIOUVILLE EQUATION 220 12.1.3
LINEARIZED ORBITAL CURRENT DENSITY 221
IMAGE 6
XVI CONTENTS
12.1.4 CALCULATION OF THE MEAN CURRENT DENSITY
IN THE # 0 -BASIS 222
12.2 THE NONLOCAL LINEAR RESPONSE TENSOR 224
12.2.1 ONE-ELECTRON APPROXIMATION 224
12.2.2 MANY-BODY APPROACH 227
12.3 TENSOR PRODUCT STRUCTURE OF THE ORBITAL RESPONSE TENSOR 229 12.4
GAUGE INVARIANCE OF THE LINEARIZED RESPONSE 232
12.5 REMARKS ON THE LOW- AND HIGH-FREQUENCY RESPONSES 236
13 MICROSCOPIC EWALD-OSEEN EXTINCTION THEOREM: COUPLED-ANTENNA THEORY
239
13.1 EXTINCTION THEOREM FOR TRANSVERSE DYNAMICS 239
13.1.1 INTEGRAL RELATION BETWEEN FIELD AND CURRENT DENSITY 239 13.1.2
EWALD-OSEEN EXTINCTION THEOREM 242
13.2 INTEGRAL EQUATIONS 244
13.3 COUPLED-ANTENNA THEORY 245
13.3.1 MATRIX EQUATION PROBLEM FOR THE LOCAL FIELD 245 13.3.2
LOCAL-FIELD RESONANCES 249
13.4 TWO-LEVEL SYSTEM: SINGLE ANTENNA DYNAMICS 251
14 TRANSVERSE AND COVARIANT ELECTROMAGNETIC PROPAGATORS: PRINCIPAL
VOLUME AND SELF-FIELD DYADICS 255
14.1 TRANSVERSE PROPAGATOR FOR THE ELECTRIC FIELD 255
14.1.1 SPECTRAL REPRESENTATION 255
14.1.2 GENUINE TRANSVERSALITY 257
14.1.3 SPACE-TIME FORM: CAUSALITY AND SPACE-LIKE NEAR-FIELD COUPLING 258
14.2 EIGENVECTOR EXPANSION OF PROPAGATORS 263
14.2.1 DISTRIBUTION THEORY 263
14.2.2 TRANSVERSE EIGENVECTOR EXPANSION OVER A FINITE DOMAIN 264
14.2.3 PLANE-WAVE EIGENVECTOR EXPANSION OVER AN INFINITE DOMAIN 266
14.3 CONTRACTION GEOMETRY AND TRANSVERSE SELF-FIELD DYNAMICS 267
14.3.1 VOLUME AND SURFACE INTEGRAL CONTRIBUTIONS TO THE TRANSVERSE
ELECTRIC FIELD 268
14.3.2 THE CONNECTION BETWEEN THE VOLUME INTEGRAL AND THE EXTERIOR
SOLUTION FOR THE TRANSVERSE FIELD 273 14.3.3 SELF-FIELD DYADIC 274
14.4 PROPAGATOR PLUS SELF-FIELD ELECTRODYNAMICS IN THE RIM ZONE AND
SOURCE REGION 276
14.5 NEAR-FIELD ELECTRODYNAMICS IN SPHERICAL CONTRACTION GEOMETRY 279
14.6 RELATIVISTIC COVARIANCE OF THE HUYGENS PROPAGATOR 280
IMAGE 7
CONTENTS XVII
15 PHOTON WAVE MECHANICS: COMPLEX FIELD THEORY 283
15.1 WAVE MECHANICS AND THE EINSTEIN-DE BROGLIE RELATIONS 283 15.2
LANDAU-PEIERLS THEORY 285
15.3 INTERLUDE: COMPLEX ANALYTICAL SIGNALS 287
15.4 COMPLEX FIELD THEORY IN THE MOMENTUM-TIME DOMAIN 290 15.4.1 PHOTON
HELICITY UNIT VECTORS 290
15.4.2 PHOTON HELICITY EIGENSTATES: WAVE FUNCTION AND WAVE EQUATIONS 292
15.4.3 PHOTON SPINOR DESCRIPTION 293
15.4.4 QUANTUM MECHANICAL MEAN VALUES OF THE PHOTON ENERGY AND MOMENTUM
295
15.5 COMPLEX FIELD THEORY IN THE SPACE-TIME DOMAIN 297 15.5.1 CARTESIAN
PHOTON SPIN OPERATOR: HELICITY OPERATOR 297 15.5.2 THE NONLOCAL HAMILTON
OPERATOR OF THE PHOTON 300
15.6 PHOTON PROBABILITY CURRENT DENSITY AND THE ASSOCIATED OPERATOR.
.302 15.7 THE NONLOCAL RELATION BETWEEN FIELD VECTORS AND PHOTON WAVE
FUNCTION 304
16 PHOTON WAVE MECHANICS: ENERGY WAVE FUNCTION AND FOUR-POTENTIAL
THEORIES 307
16.1 PHOTON ENERGY WAVE FUNCTION FORMALISM 307
16.1.1 RIEMANN-SILBERSTEIN APPROACH TO CLASSICAL ELECTROMAGNETICS IN
FREE SPACE 307
16.1.2 DYNAMICAL EQUATION FOR THE PHOTON ENERGY WAVE FUNCTION 309
16.1.3 QUANTUM MECHANICAL MEAN VALUE OF THE PHOTON ENERGY-MOMENTUM
OPERATOR IN RECIPROCAL SPACE 312
16.1.4 LORENTZ-INVARIANT INTEGRATION ON THE LIGHT CONE 315 16.2 RELATION
BETWEEN THE ENERGY WAVE FUNCTION AND COMPLEX FIELD FORMALISMS IN DIRECT
SPACE 317
16.3 WAVE MECHANICS OF LONGITUDINAL AND SCALAR PHOTONS: STANDARD THEORY
319
16.3.1 COMPLEX FIELD THEORY IN TERMS OF THE TRANSVERSE VECTOR POTENTIAL
319
16.3.2 LONGITUDINAL AND SCALAR PHOTON WAVE FUNCTIONS, AND THEIR RELATED
WAVE EQUATIONS 320 16.3.3 IDENTITY OF THE LONGITUDINAL AND SCALAR
PHOTONS 322 16.3.4 QUANTUM MECHANICAL MEAN VALUES
OF THE LONGITUDINAL AND SCALAR PHOTON ENERGIES 323 16.4 WAVE MECHANICS
OF GAUGE AND NEAR-FIELD PHOTONS 324 16.4.1 TRANSVERSE PHOTON
SCHROEDINGER-LIKE EQUATIONS IN DIRECT AND RECIPROCAL SPACE 325
16.4.2 LONGITUDINAL AND SCALAR PHOTONS ONCE MORE 326
IMAGE 8
XVIII CONTENTS
16.4.3 GAUGE AND NEAR-FIELD PHOTONS 327
16.4.4 GAUGE TRANSFORMATIONS WITHIN THE LORENZ GAUGE 328 16.4.5
ELIMINATION OF THE GAUGE PHOTON 329
17 PHOTON ANGULAR MOMENTUM 333
17.1 BODILY ROTATION OF SCALAR AND VECTOR FIELDS 334
17.2 ORBITAL AND SPIN PARTS OF THE PHOTON ANGULAR MOMENTUM 337 17.2.1
DIVISION OF THE ANGULAR MOMENTUM OF THE TRANSVERSE ELECTROMAGNETIC FIELD
337
17.2.2 QUANTUM MECHANICAL MEAN VALUES OF THE ORBITAL AND SPIN ANGULAR
MOMENTA IN THE COMPLEX FIELD THEORY 339
17.2.3 QUANTUM MECHANICAL MEAN VALUES OF THE ORBITAL AND SPIN ANGULAR
MOMENTA IN THE ENERGY WAVE FUNCTION FORMALISM 341
17.3 MORE ON THE PHOTON SPIN AND HELICITY 342
17.3.1 ARE L AND S SEPARATE OBSERVABLES FOR A PHOTON? 342
17.3.2 QUANTUM MECHANICAL MEAN VALUE OF THE CARTESIAN PHOTON SPIN
OPERATOR 343
17.3.3 PROJECTED PHOTON SPIN OPERATOR 345
17.3.4 EIGENVECTORS AND EIGENVALUES OF THE PHOTON HELICITY OPERATOR 346
18 PHOTON EMISSION FROM MICRO- AND MESOSCOPIC SOURCES: NEAR-FIELD
ASPECTS 349
18.1 MICROSCOPIC ELECTRODYNAMICS BASED ON D- AND H-FIELDS 350
18.1.1 NEW MICROSCOPIC FIELD EQUATIONS 350
18.1.2 DUALITY BETWEEN OLD AND NEW TRANSVERSE ELECTRODYNAMICS: NEW WAVE
EQUATIONS 351
18.2 THE PHOTON EMBRYO CONCEPT 352
18.2.1 DYNAMICAL PHOTON WAVE FUNCTION VARIABLES 352 18.2.2 DYNAMICAL
EQUATIONS FOR THE PHOTON WAVE FUNCTION VARIABLES 354
18.2.3 PHOTON EMBRYO IN MOMENTUM SPACE 355
18.3 ONE-PHOTON SOURCES 357
18.4 PROPAGATOR DESCRIPTION OF PHOTON EMBRYO IN SPACE-TIME 359
18.4.1 REMARKS ON THE CLASSICAL SOURCE TERM W(R,T) 359 18.4.2 PROPAGATOR
SOLUTIONS OF THE WAVE EQUATIONS FORZ (R,F) AND J/(R,F) 359
18.4.3 PROPAGATION OF EMBRYO STATE 360
IMAGE 9
CONTENTS XIX
18.5 GAUGE AND NEAR-FIELD PHOTON EMBRYOS 361
18.5.1 DYNAMICAL EQUATIONS FOR G- AND NF-PHOTON VARIABLES 361 18.5.2
TIME REVERSAL: SOLUTION OF THE DYNAMICAL EQUATIONS FOR THE G- AND
NF-VARIABLES 363
19 EIKONAL THEORY FOR TRANSVERSE PHOTONS AND MASSIVE PARTICLES OF ZERO
SPIN 365
19.1 FOUNDATIONS OF GEOMETRICAL OPTICS 366
19.1.1 MACROSCOPIC MAXWELL EQUATIONS 366
19.1.2 EIKONAL EQUATION AND ENERGY TRANSPORT 367
19.2 MASSIVE TRANSVERSE PHOTON 370
19.2.1 MICROSCOPIC TRANSVERSE ELECTRODYNAMICS AT HIGH FREQUENCIES 370
19.2.2 QUANTUM MECHANICAL PHOTON WAVE EQUATION IN A HOMOGENEOUS MEDIUM
372
19.2.3 ENERGY-MOMENTUM RELATION: MASS OF TRANSVERSE PHOTON 373
19.2.4 PHOTON MASS IN THE ENERGY WAVE FUNCTION FORMALISM 374 19.3 PHOTON
EIKONAL GRADIENT: LOCAL PARTICLE MOMENTUM 376 19.3.1 PHOTON EIKONAL
EQUATION 376
19.3.2 LOCAL PHOTON MOMENTUM 378
19.4 HAMILTON-JACOBI FORMULATION OF CLASSICAL MECHANICS 380 19.4.1 THE
HAMILTON EQUATIONS AND THEIR DERIVATION FROM A VARIATIONAL PRINCIPLE 381
19.4.2 A PARTICULAR CANONICAL TRANSFORMATION 383
19.4.3 HAMILTON-JACOBI EQUATION FOR HAMILTON'S PRINCIPAL FUNCTION 384
19.4.4 HAMILTON-JACOBI EQUATION FOR HAMILTON'S CHARACTERISTIC FUNCTION
385
19.5 EIKONAL THEORY OF CHARGED PARTICLES IN QUANTUM MECHANICS 386 19.5.1
NONRELATIVISTIC HAMILTON-JACOBI EQUATION 386 19.5.2 QUANTUM POTENTIAL
AND PROBABILITY FLUID FLOW 389 19.5.3 RELATIVISTIC HAMILTON-JACOBI
EQUATION:
PARTICLE OF ZERO SPIN 390
20 SPIN-1/2 CURRENTS: SPATIAL PHOTON LOCALIZATION IN EMISSION FROM A
PURE SPIN TRANSITION 395
20.1 SPIN-1/2 CURRENT DENSITY 395
20.1.1 DIRAC EQUATION IN MINIMAL COUPLING FORM 396 20.1.2 FULLY
RELATIVISTIC DIRAC CURRENT DENSITY 398
20.1.3 WEAKLY RELATIVISTIC PAULI SPIN CURRENT DENSITY 399 20.2 SPIN
SOURCE FOR PHOTONS: ABSENCE OF THE RIM ZONE 403
20.3 PHOTON EMISSION FROM SPIN-1/2 TRANSITIONS 406
20.3.1 ELECTROMAGNETIC FAR FIELD 406
20.3.2 EMISSION FROM AN ISOTROPIE MICROSCOPIC SOURCE 407
IMAGE 10
XX CONTENTS
21 ONE-PARTICLE POSITION OPERATORS AND SPATIAL LOCALIZATION 411 21.1
NONRELATIVISTIC PARTICLE 411
21.2 MASSIVE RELATIVISTIC PARTICLE OF ZERO SPIN 412
21.2.1 POSITION OPERATOR 412
21.2.2 EIGENSTATES OF THE POSITION OPERATOR: LOCALIZATION IN
CONFIGURATION SPACE 413
21.3 MASSLESS SPIN-ONE PARTICLE (PHOTON) 417
21.3.1 TRANSVERSE EIGENSTATES IN MOMENTUM SPACE 417 21.3.2 DYADIC PHOTON
POSITION OPERATOR 418
21.3.3 THE PHOTON POSITION OPERATOR PROBLEM IN CONFIGURATION SPACE 419
PART III QUANTUM ELECTRODYNAMIC THEORY
22 NEAR FIELDS AND QED 423
22.1 THE ZOO OF PHOTONS 423
22.1.1 ONE-PHOTON WAVE PACKETS 425
22.2 NEAR-FIELD COMMUTATORS 425
22.3 MAXWELL-LORENTZ OPERATOR EQUATIONS: COULOMB AND POINCARE GAUGES 426
22.4 COVARIANT FIELD PROPAGATORS 428
22.5 PHOTON EMISSION FROM ATOMS AND MESOSCOPIC OBJECTS 429 22.6 VIRTUAL
TRANSVERSE PHOTON EXCHANGE IN NEAR-FIELD ELECTRODYNAMICS 432
22.7 EXCHANGE OF SCALAR PHOTONS 433
22.8 COHERENT STATES OF EVANESCENT FIELDS 433
23 THE ROUTE TO THE MAXWELL-LORENTZ OPERATOR EQUATIONS IN THE COULOMB
GAUGE 435
23.1 PLANE-WAVE QUANTIZATION OF THE TRANSVERSE ELECTROMAGNETIC FIELD 435
23.1.1 THE CLASSICAL FIELD VECTORS 435
23.1.2 THE CLASSICAL FIELD ENERGY AND MOMENTUM IN FREE SPACE 438
23.1.3 THE CLASSICAL SPIN OF THE FREE FIELD 440
23.1.4 QUANTIZATION SCHEME FOR THE RADIATION FIELD: TRANSVERSE FIELD
OBSERVABLES 442
23.1.5 HAMILTON, MOMENTUM AND SPIN OPERATORS FOR THE TRANSVERSE
ELECTROMAGNETIC FIELD 444
23.1.6 MONOCHROMATIC PLANE-WAVE PHOTONS: A BRIEF REVIEW 445 23.2
TEMPORAL EVOLUTION OF THE GLOBAL FIELD-MATTER SYSTEM 448 23.2.1 STATE
SPACE 448
23.2.2 TOTAL NONRELATIVISTIC HAMILTONIAN IN THE COULOMB GAUGE 448
23.2.3 THE SCHROEDINGER PICTURE 449
IMAGE 11
CONTENTS XXI
23.2.4 THE HEISENBERG PICTURE 450
23.2.5 THE INTERACTION PICTURE 451
23.3 THE QUANTIZED NEWTON-LORENTZ EQUATION 452
23.4 THE QUANTIZED MAXWELL-LORENTZ EQUATIONS IN THE COULOMB GAUGE 455
23.4.1 EQUATION OF MOTION FOR THE ANNIHILATION OPERATOR, A QS 455
23.4.2 EQUATIONS OF MOTIONS FOR THE TRANSVERSE ELECTRIC ( T ) AND
MAGNETIC (B) FIELD OPERATORS 458 23.4.3 LONGITUDINAL ELECTRIC FIELD
OPERATOR 460
24 FIELD COMMUTATORS AND INTEGRAL REPRESENTATION OF VARIOUS COVARIANT
PROPAGATORS 461
24.1 THE JORDAN-PAULI AND FEYNMAN SCALAR PROPAGATORS 462 24.2 FREE-FIELD
COMMUTATORS FOR FIELDS TAKEN AT DIFFERENT SPACE-TIME POINTS 463
24.3 FIELD COMMUTATORS IN THE PRESENCE OF FIELD-MATTER INTERACTION 468
24.3.1 EQUAL-TIME COMMUTATORS 468
24.3.2 WEIGHTED AVERAGE VALUES OF FIELDS AND COMMUTATORS 469
24.3.3 QUANTUM MECHANICAL MEAN VALUE AND VARIANCE OF THE MEAN FIELD 470
24.4 CONTOUR INTEGRAL REPRESENTATIONS OF COVARIANT SCALAR PROPAGATORS
472
24.4.1 THE JORDAN-PAULI PROPAGATOR 472
24.4.2 THE FEYNMAN PROPAGATOR 473
25 ELECTRODYNAMICS IN THE POINCARE GAUGE 477
25.1 THE POINCARE GAUGE 478
25.2 A SPECIFIC CHOICE FOR THE GENERALIZED POLARIZATION AND
MAGNETIZATION 480
25.2.1 POLARIZATION FIELD 480
25.2.2 MAGNETIZATION FIELD 482
25.3 LAGRANGIANS IN THE COULOMB AND POINCARE GAUGES 484 25.3.1
NONRELATIVISTIC STANDARD LAGRANGIAN AND ITS GAUGE TRANSFORMATION 484
25.3.2 THE POWER-ZIENAU-WOOLLEY TRANSFORMATION 485 25.3.3 ON THE
ELIMINATION OF THE REDUNDANCY FROM THE STANDARD LAGRANGIAN 486
25.3.4 COULOMB LAGRANGIAN: REGROUPING OF PARTS 487 25.3.5 POINCARE
INTERACTION LAGRANGIAN 488
25.3.6 MULTIPOLE INTERACTION LAGRANGIAN 489
25.4 CONJUGATE MOMENTA: COULOMB AND POINCARE HAMILTONIANS 490 25.4.1
CONJUGATE PARTICLE MOMENTUM 490
25.4.2 CONJUGATE FIELD MOMENTUM 490
25.4.3 HAMILTONIANS 491
IMAGE 12
XXII CONTENTS
25.5 QUANTUM DESCRIPTION IN THE POINCARE GAUGE 493
25.5.1 QUANTUM REPRESENTATIONS RELATED BY A UNITARY TRANSFORMATION: A
BRIEF REVIEW 493
25.5.2 THE UNITARY TRANSFORMATION RELATING THE QUANTUM DESCRIPTIONS IN
THE COULOMB AND POINCARE GAUGES 495
25.5.3 TRANSFORMATION OF VARIOUS PHYSICAL QUANTITIES 496 25.5.4
CANONICAL QUANTIZATION: HAMILTON OPERATOR 499
26 PHOTON-FIELD OPERATORS: WAVE-PACKET PHOTONS 501
26.1 FREE PHOTON-FIELD OPERATORS 502
26.2 SINGLE-PHOTON STATES: RELATION TO PHOTON WAVE MECHANICS 504 26.3
LOCAL AND GLOBAL BILINEAR OPERATORS: NONSTATIONARY ONE-PHOTON STATES 506
26.4 WAVE-PACKET PHOTON OPERATORS AND STATES 507
26.5 MAXWELL-LORENTZ OPERATOR EQUATIONS IN THE POINCARE GAUGE 510 26.6
MATTER-COUPLED PHOTON-FIELD OPERATORS 511
26.7 PHOTON EMBRYO IN SPONTANEOUS EMISSION 512
27 PHOTON EMISSION FROM ATOMS: ELEMENTS OF THE NONRELATIVISTIC QED
DESCRIPTION 515
27.1 INTEGRAL RELATIONS BETWEEN FIELD AND PARTICLE OPERATORS 516 27.1.1
ON THE NONRELATIVISTIC LAMB SHIFT AND SPONTANEOUS EMISSION 516
27.1.2 PROPAGATOR CONNECTION BETWEEN THE PHOTON-FIELD AND
SOURCE-PARTICLE OPERATORS 518 27.2 FIELD RADIATION FROM SINGLE-PARTICLE
SOURCE 520
27.2.1 SECOND-QUANTIZATION OF SOURCE CURRENT DENSITY: FLIP OPERATORS 520
27.2.2 THE RETARDED RELATION BETWEEN FIELD AND FLIP OPERATORS 522
27.2.3 SINGLE-ELECTRON SPONTANEOUS EMISSION: NEGLECT OF DIAMAGNETISM 523
27.3 THE ELECTRIC DIPOLE HAMILTONIAN AND THE ASSOCIATED OPERATOR 525
27.3.1 LONG-WAVELENGTH APPROXIMATION OF THE CLASSICAL POINCARE
HAMILTONIAN 525
27.3.2 LONG-WAVELENGTH UNITARY TRANSFORMATION OF THE COULOMB HAMILTON
OPERATOR 527
27.4 TWO-LEVEL ATOM 530
27.4.1 RAISING AND LOWERING OPERATORS 531
27.4.2 PAULI OPERATORS 532
27.4.3 ELECTRON-FIELD OPERATORS 533
27.4.4 ELECTRIC-DIPOLE HAMILTONIAN 535
IMAGE 13
CONTENTS XXIII
27.5 DYNAMICAL EQUATIONS FOR A COUPLED TWO-LEVEL ATOM PLUS FIELD SYSTEM
537
27.5.1 HEISENBERG EQUATION OF MOTION FOR THE ATOMIC FLIP OPERATOR, B 537
27.5.2 HEISENBERG EQUATION OF MOTION FOR THE FIELD ANNIHILATION
OPERATOR, A QS 538
27.6 SPONTANEOUS EMISSION AND LAMB SHIFT: HEURISTIC APPROACH 539 27.6.1
ROTATING-WAVE APPROXIMATION 539
27.6.2 MARKOV APPROXIMATION 540
27.6.3 THE SPONTANEOUS DECAY RATE 542
27.6.4 THE LAMB-SHIFT PARAMETER 544
27.6.5 THE RADIATED TRANSVERSE FIELD 546
27.6.6 THE {B, ^J-ANTICOMMUTATOR PROBLEM 549
27.6.7 RELATION BETWEEN THE SPONTANEOUS DECAY RATE AND THE TRANSVERSE
PROPAGATOR 550
28 PARTICLE-PARTICLE INTERACTION BY TRANSVERSE PHOTON EXCHANGE 553 28.1
MULTIPOLE EXPANSION OF THE COULOMB INTERACTION ENERGY 554 28.2
PERTURBATION BY AN EFFECTIVE ELECTRONIC HAMILTONIAN 556 28.3
SINGLE-PHOTON EXCHANGE BETWEEN TWO CHARGED PARTICLES 560
28.3.1 QUALITATIVE ANALYSIS OF THE EFFECTIVE HAMILTONIAN TO SECOND ORDER
561
28.3.2 DELAY AND MAGNETIC CORRECTIONS TO THE COULOMB INTERACTION 566
28.3.3 MOMENTUM EXCHANGE 569
28.4 VAN DER WAALS INTERACTION BETWEEN TWO NEUTRAL PARTICLES 571 28.4.1
INTERACTION FROM THE POWER-ZIENAU-WOOLLEY POINT OF VIEW 571
28.4.2 EXCHANGE OF VIRTUAL TRANSVERSE PHOTONS 574
28.5 CASIMIR EFFECT: PARTICLE-SURFACE INTERACTION 578
28.6 REMARKS ON THE CASIMIR-POLDER EFFECT 581
29 PHOTONS IN A MANIFESTLY LORENTZ-COVARIANT THEORY 583
29.1 COVARIANT FORMULATION OF CLASSICAL FREE-FIELD DYNAMICS 584 29.1.1
COVARIANT NOTATION 584
29.1.2 THE FREE MAXWELL EQUATIONS IN COVARIANT FORM 585 29.1.3 LAGRANGE
EQUATIONS FOR THE FREE FIELD: STANDARD APPROACH 586
29.1.4 MODIFIED FIELD LAGRANGIAN DENSITY 587
29.2 PLANE-WAVE EXPANSION OF THE FOUR-POTENTIAL 589
29.2.1 FOUR-COMPONENT POLARIZATION VECTORS 589
29.2.2 GAUGE, NEAR-FIELD, AND TRANSVERSE FOUR-COMPONENT POTENTIALS 590
29.2.3 LORENZ CONDITION: GAUGE ARBITRARINESS 592
29.2.4 ELECTROMAGNETIC FIELD HAMILTONIAN 593
IMAGE 14
XXIV CONTENTS
29.3 COVARIANT FIELD QUANTIZATION 595
29.3.1 HAMILTON OPERATOR AND COMMUTATOR RELATIONS 595 29.3.2 SCALAR
PHOTONS: THE PROBLEM OF NEGATIVE NORMS 597 29.3.3 GUPTA-BLEULER-LORENZ
CONDITION 598
29.3.4 NEAR-FIELD AND GAUGE PHOTON QUANTA: COMMUTATORS AND HAMILTON
OPERATOR 600
29.4 COVARIANT QUANTIZATION WITH AN INDEFINITE METRIC 602
29.4.1 NEW SCALAR PRODUCT AND NEW ADJOINING OPERATOR, OE 602
29.4.2 CHOICE OF NEW METRIC 603
29.4.3 NEAR-FIELD AND GAUGE PHOTONS IN THE NEW METRIC 605 29.5 A SS
(X)-COMMUTATORS AND THE FEYNMAN PHOTON PROPAGATOR 607 29.5.1 COVARIANT
COMMUTATION RELATIONS 607
29.5.2 EQUAL-TIME COMMUTATION RELATIONS 608
29.5.3 THE FEYNMAN PHOTON PROPAGATOR 609
30 MATTER-ATTACHED QUANTIZED FIELDS 611
30.1 ANALYSIS OF THE COVARIANT PHOTON PROPAGATOR 612
30.1.1 COMBINED EXCHANGE OF LONGITUDINAL AND SCALAR PHOTONS 612
30.1.2 NEAR-FIELD AND GAUGE PHOTON EXCHANGE 615
30.2 FIELD-PARTICLE INTERACTION IN COVARIANT NOTATION 617
30.2.1 INTERACTION LAGRANGIAN DENSITY AND WAVE EQUATION 617 30.2.2
RETARDED AND ADVANCED PROPAGATORS: IN- AND OUT-STATES 618
30.3 INTERACTION BETWEEN TWO FIXED CHARGES: EXCHANGE OF SCALAR PHOTONS
621
30.3.1 PRESCRIBED PARTICLE DYNAMICS: HAMILTONIAN FOR FIELD EVOLUTION 621
30.3.2 ENERGY SHIFT OF THE GROUND STATE OF THE FIELD 622
30.3.3 REINTERPRETATION OF COULOMB'S LAW 625
30.4 COULOMB INTERACTION: THE NEAR-FIELD AND GAUGE PHOTON PICTURE .
.627 30.5 CLASSICAL POTENTIALS GENERATED BY A PRESCRIBED SHEET SOURCE
629 30.5.1 SHEET CURRENT DENSITY 629
30.5.2 LONGITUDINAL AND SCALAR PARTS OF THE CLASSICAL FOUR-POTENTIAL 631
30.5.3 QUASI-STATIC REGIME 635
30.5.4 SHEET RIM ZONE 636
30.6 QUANTUM FIELD RADIATED BY A CLASSICAL SOURCE 636
30.6.1 CURRENT DENSITY WITHOUT QUANTUM FLUCTUATIONS 636 30.6.2
HEISENBERG EQUATIONS OF MOTION FOR THE ANNIHILATION OPERATORS {A R {Q\
T)} 637
IMAGE 15
CONTENTS XXV
30.6.3 COHERENT FIELD STATE 638
30.6.4 COHERENT SCALAR AND LONGITUDINAL PHOTON RADIATION FROM A SHEET
SOURCE 639
REFERENCES 643
INDEX 653 |
| any_adam_object | 1 |
| author | Keller, Ole 1945- |
| author_GND | (DE-588)1020334053 |
| author_facet | Keller, Ole 1945- |
| author_role | aut |
| author_sort | Keller, Ole 1945- |
| author_variant | o k ok |
| building | Verbundindex |
| bvnumber | BV039661673 |
| classification_rvk | UH 1000 UH 5600 UO 5600 UO 5610 |
| ctrlnum | (OCoLC)690089531 (DE-599)DNB100790416X |
| dewey-full | 535.15 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 535 - Light and related radiation |
| dewey-raw | 535.15 |
| dewey-search | 535.15 |
| dewey-sort | 3535.15 |
| dewey-tens | 530 - Physics |
| discipline | Physik |
| format | Book |
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| id | DE-604.BV039661673 |
| illustrated | Illustrated |
| indexdate | 2024-07-21T00:14:00Z |
| institution | BVB |
| isbn | 9783642174094 3642174094 9783642174100 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-024511044 |
| oclc_num | 690089531 |
| open_access_boolean | |
| owner | DE-11 DE-634 DE-19 DE-BY-UBM DE-703 DE-83 |
| owner_facet | DE-11 DE-634 DE-19 DE-BY-UBM DE-703 DE-83 |
| physical | XXV, 667 S. graph. Darst. |
| publishDate | 2011 |
| publishDateSearch | 2011 |
| publishDateSort | 2011 |
| publisher | Springer |
| record_format | marc |
| series2 | Nano-optics and nanophotonics |
| spelling | Keller, Ole 1945- Verfasser (DE-588)1020334053 aut Quantum theory of near-field electrodynamics Ole Keller Berlin [u.a.] Springer 2011 XXV, 667 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Nano-optics and nanophotonics Quantenelektrodynamik (DE-588)4047982-1 gnd rswk-swf Nahfeldoptik (DE-588)4739877-2 gnd rswk-swf Quantenoptik (DE-588)4047990-0 gnd rswk-swf Elektrodynamik (DE-588)4014251-6 gnd rswk-swf Nahfeldoptik (DE-588)4739877-2 s Elektrodynamik (DE-588)4014251-6 s Quantenelektrodynamik (DE-588)4047982-1 s Quantenoptik (DE-588)4047990-0 s DE-604 Erscheint auch als Online-Ausgabe Quantum Theory of Near-Field Electrodynamics X:MVB text/html http://deposit.dnb.de/cgi-bin/dokserv?id=3554074&prov=M&dok_var=1&dok_ext=htm Inhaltstext DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=024511044&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Keller, Ole 1945- Quantum theory of near-field electrodynamics Quantenelektrodynamik (DE-588)4047982-1 gnd Nahfeldoptik (DE-588)4739877-2 gnd Quantenoptik (DE-588)4047990-0 gnd Elektrodynamik (DE-588)4014251-6 gnd |
| subject_GND | (DE-588)4047982-1 (DE-588)4739877-2 (DE-588)4047990-0 (DE-588)4014251-6 |
| title | Quantum theory of near-field electrodynamics |
| title_auth | Quantum theory of near-field electrodynamics |
| title_exact_search | Quantum theory of near-field electrodynamics |
| title_full | Quantum theory of near-field electrodynamics Ole Keller |
| title_fullStr | Quantum theory of near-field electrodynamics Ole Keller |
| title_full_unstemmed | Quantum theory of near-field electrodynamics Ole Keller |
| title_short | Quantum theory of near-field electrodynamics |
| title_sort | quantum theory of near field electrodynamics |
| topic | Quantenelektrodynamik (DE-588)4047982-1 gnd Nahfeldoptik (DE-588)4739877-2 gnd Quantenoptik (DE-588)4047990-0 gnd Elektrodynamik (DE-588)4014251-6 gnd |
| topic_facet | Quantenelektrodynamik Nahfeldoptik Quantenoptik Elektrodynamik |
| url | http://deposit.dnb.de/cgi-bin/dokserv?id=3554074&prov=M&dok_var=1&dok_ext=htm http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=024511044&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT kellerole quantumtheoryofnearfieldelectrodynamics |