Introduction to classical and quantum field theory:
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Wiley-VCH
2009
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| Physical Description: | XIV, 292 S. graph. Darst. |
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| 100 | 1 | |a Ng, Tai-Kai |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Introduction to classical and quantum field theory |c Tai-Kai Ng |
| 264 | 1 | |a Weinheim |b Wiley-VCH |c 2009 | |
| 300 | |a XIV, 292 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 0 | |a Physics textbook | |
| 650 | 4 | |a Feldtheorie - Lehrbuch | |
| 650 | 4 | |a Condensed matter |v Problems, exercises, etc | |
| 650 | 4 | |a Condensed matter |v Textbooks | |
| 650 | 4 | |a Quantum field theory |v Problems, exercises, etc | |
| 650 | 4 | |a Quantum field theory |v Textbooks | |
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Contents
Acknowledgements
V
Introduction
to Classical and Quantum Field Theory
XIII
Part One
1
1
Introduction
3
1.1
What is a Field Theory?
3
1.1.1
Mathematical Description
3
1.2
Basic Mathematical Tools in (Classical) Field Theory
5
1.2.1
Solution of Field Equations of Motion
5
1.2.1.1
Eigenfunction Expansion Method
6
1.2.1.2
Eigenfunction Expansions for Green s Functions
7
1.2.1.3
A Variant of the Above Method: Initial Condition Problem
8
1.2.1.4
Comment on
Non-
Linear Equations of Motion
10
1.2.2
Evaluation of Partition Function for Quadratic Field Theories
10
1.2.2.1
Non-Linear Energy Functional
13
1.2.2.2
Continuum Limit
13
1.2.2.3
Constraints
14
2
Basics of Classical Field Theory
17
2.1
Lagrangian
Formulation
for Classical Mechanics/Field
Theory
17
2.1.1
Basic
Ansatz:
The Principle of Least Action
17
2.1.1.1
Conservation of Energy and Momentum
18
2.1.1.2
Galilean
Invariance
and the Most General Form
of Lagrangian
19
2.1.1.3
Constraints
21
2.1.1.4
Lagrangian Formulation for Classical Field Theory
21
2.1.1.5
Space-Time Symmetric Lagrangian Formulation
23
2.2
Conservation Laws in Continuum Field Theory (Noether s
Theorem)
24
Vili
Contents
2.2.1
Energy-Momentum Conservation
24
2.2.1.1
Internal Symmetry and Noether s Theorem
26
2.2.2
More Complicated Internal Symmetries
27
References
28
3
Quantization of Classical Field Theories (I)
29
3.1
Canonical Quantization of Scalar Fields: Bosonic Systems
29
3.1.1
General Quadratic Hamiltonian and Bosons
31
3.1.2
Interaction Between Particles
33
3.1.3
Continuum Limit of Lattice Field Theory
34
3.2
Introduction to Quantum Statistics
35
3.2.1
Fock Space for Bosons and
Fermions
36
3.2.2
Introduction to
Grassmann
Field and Quantum Field Theory
for
Fermions
38
3.3
Path Integral Quantization of Mechanics and Field Theory
41
3.3.1
Imaginary-Time Path Integral and Partition Function
43
3.3.2
Application to Quantum Field Theory
45
References
47
4
Quantization of Classical Field Theories (II)
49
4.1
Path Integral Quantization in Coherent State Representations
of Bosons and
Fermions
49
4.1.1
Imaginary Time and Partition Function
51
4.1.1.1
Quantum Field Theory for Bosons
51
4.1.1.2
Quantum Field Theory for
Fermions
52
4.2
Two Simple Examples of QFT
54
4.2.1
Phonons
54
4.2.1.1
Continuum Limit
55
4.2.2
Dirac
Fermions
in ID
56
4.2.2.1
Covariant form of Dirac equation
59
4.2.3
Quantization of Dirac Equation
60
4.2.3.1
Lattice Dirac
Fermions
61
4.3
Simple Applications of Path Integral Formulation
63
4.4
Symmetry and Conservation Laws in Quantum Field Theory
67
References
69
Part Two
71
5
Perturbation Theory, Variational Approach and Correlation Functions
73
5.1
Introduction to Perturbation Theory
73
5.1.1
Path Integral Approach
74
5.1.1.1
Perturbation Theory for Interacting Systems
76
5.1.1.2
Wick s Theorem
77
5.1.2
Dyson s Approach
79
5.1.2.1
Time-Evolution Operator at Imaginary Time
81
Contents
IX
5.1.2.2
Perturbation
Expansion
for S Matrix
81
5.1.2.3
Wick s Theorem in Dyson s Approach
83
5.1.2.4
Example: One-Particle Green s Function
84
5.1.2.5
Perturbation Expansion for One-Particle Green s Function
86
5.1.2.6
Spectral Representation
89
5.2
Variational Approach and Perturbation Theory
92
5.2.1
Example: Hartree-Fock Approximation
93
5.3
Some General Properties of Correlation Functions
95
5.3.1
Linear Response Theory
95
5.3.2
Temperature and Causal Correlation Functions
99
5.3.3
Fluctuation-Dissipation Theorem
101
References
105
6
Introduction to Berry Phase and Gauge Theory
107
6.1
Introduction to Berry Phase
207
6.1.1
Berry Phase for a Simple Quantum System
107
6.1.2
Berry Phase and Particle Statistics 111
6.1.3
Berry Phase and U(l) Gauge Theory
112
6.1.3.1
Relation Between
Αμ
and Berry Phase
113
6.1.4
Electromagnetism
as Gauge Theory
114
6.2
Singular Gauge Potentials and Angular Momentum Quantization
116
6.2.1 Aharonov-Bohm (AB)
Effect
116
6.2.2
Alternative Description of the Problem
118
6.2.3
Magnetic
Monopole
and Angular Momentum Quantization
118
6.2.3.1
Geometrical Theory of Angular Momentum
119
6.2.3.2
Berry Phase and Angular Momentum Quantization
121
6.2.3.3
Quantization of Magnetic
Monopole 121
6.2.3.4
Two Dimensions
123
6.2.3.5
Angular Momentum: Statistics Theorem
123
6.3
Quantization of Electromagnetic Field
124
6.3.1
Canonical Quantization
124
6.3.2
Path Integral Quantization
126
6.3.3
Gauge Problem
127
References
128
7
Introduction to Effective Field Theory, Phases, and Phase
Transitions
129
7.1
Introduction to Effective Field Theory: Boltzmann Equation
and Fluid Mechanics
129
7.1.1
Fluid Mechanics
132
7.1.1.1
Friction and Viscosity
134
7.1.1.2
Limitation of Hydrodynamics: An Example
135
7.2
Landau Theory of Phases and Phase Transitions
136
7.2.1
Order Parameters
136
7.2.1.1
Paramagnetic
<-*
Ferromagnetic Transition
137
X
Contents
7.2.1.2 Liquid <-+
Solid Transition
137
7.2.1.3
Phase Transitions and Broken Ergodicity
137
7.2.2
Landau s Phenomenological Theory of Phase Transitions
139
7.2.2.1
Weakly First-Order Phase Transition
141
7.2.2.2
Effective Free Energies in Landau Theory
143
7.2.2.3
Continuum Limit and Landau Theory
145
7.2.2.4
Quantum Phase Transitions
146
7.3
Other Examples of Effective Classical and Quantum
Field Theories
147
7.3.1
Projective
Hubert Space (Mori) Approach and Correlation
Functions
148
7.3.2
Quantum Principle of Least Action and Applications
150
7.3.2.1
Quasi-particles
152
7.3.3
(Generalized)
Langevin
and Fokker-Planck Equations
153
7.3.3.1
Fokker-Planck Equation
156
References
257
8 Solitons,
Instantons,
and Topology in QFT
159
8.1
Introduction to
Solitons 159
8.1.1
Stability of
Solitons
and Topology
162
8.1.1.1
Topological Index for One-Dimensional Scalar Fields
164
8.1.2
Multi-Kink Solutions and Difference Between Solitary
Wave and Soliton
164
8.1.2.1
Quantization of Solitons/Solitary Waves
165
8.2
Introduction to
Instantons
165
8.2.1 Instantons in
ID Classical Theories
165
8.2.1.1 Instantons in
Quantum Mechanics: Quantum
Tunneling
168
8.2.2
Winding Number
169
8.3
Vortices and Kosterlitz-Thouless Transition
171
8.3.1
Low-Temperature Spin-Spin Correlation Function
174
8.3.2
Kosterlitz-Thouless Transition
175
8.3.3
Screening and KT Transition
177
8.3.4
Vortices in Superconductors and
Superfluide
279
8.4
Skyrmions and
Monopoles
280
8.4.1
Spinor (CPi)
Representation
183
8.4.2
Meaning of Gauge Field
284
8.4.3
Magnetic
Monopoles
285
References
186
Part Three A Few Examples
287
9
Simple Boson Liquids: Introduction to Superfluidity
289
9.1
Saddle-Point Approximation: Semiclasskal Theory for
Interacting Bosons
289
Contents
XI
9.1.1 Semidassical Approximation
(using
One-Partide QM
as Example)
189
9.1.2
Density-Density Response Function and One-Particle
Green s Function
296
9.1.2.1
A Little Bit Beyond the Semiclassical Approximation
197
9.2
Superfluidity
198
9.2.1
Bose
Condensation
198
9.2.2
Superfluid He4
199
9.2.3
Landau s Analysis for Superfluidity
199
9.2.3.1
A Free Boson Condensate is Not a Superfluid
202
9.2.3.2
A Boson Fluid with Phonon-Like Excitation Spectrum
is a Superfluid
201
9.2.3.3
Off-Diagonal Long-Range Order (ODLRO) and Collective
Motion of Superfluid
202
9.2.3.4
Two-Fluid Picture
203
9.3
Charged
Superfluide: Higgs
Mechanism and
Superconductivity
204
9.3.1 Goldstone
Theorem and Higgs Mechanism
204
9.3.2
Higgs Mechanism and Superconductivity
207
9.3.2.1
Meissner Effect (Higgs Mechanism on Gauge Field)
207
9.4
Supersolids
208
9.5
A Brief Comment Before Ending
210
References
210
10
Simple Fermion Liquids: Introduction to Fermi Liquid Theory
222
10.1
Single-Partide and Collective Excitations in
Fermi Liquids
222
10.1.1
The Spectrum of a Free Fermi Gas
212
10.1.2
Collective Modes in Fermi Liquid
213
10.1.2.1
Hubbard-Stratonovich Transformation
214
10.1.2.2
Excitation
Speerram
of Electron Gas in
RPA
218
10.1.3
Alternative Derivation for
RPA
229
10.1.4
Screening
221
10.2
Introduction to Fermi liquids and Fermi Liquid Theory
222
10.2.1
Quasi-partides and Single-Partide Green s Function
224
10.2.2
Charge and Current Carried by Quasi-particles
225
10.2.3
Two Examples of Applications
227
10.2.4
Bosonization Description of Fermi Liquid Theory
229
10.2.5
Beyond Fermi liquid Theory?
230
References
232
11
Superconductivity: BCS Theory and Beyond
233
11.1
BCS Theory for (s-wave) Superconductors: Path Integral
Approach
233
11.1.1
Semiclassical (Gaussian) Theory
237
XII Contents
11.2
BCS
Theory for (s-Wave) Superconductors: Fermion
Excitations and Hamiltonian Approach
239
11.2.1
Variational Waveftmction in BCS Theory
241
11.2.2
GL Equation and Vortex Solution
242
11.2.2.1
Flux Quantization
244
11.2.2.2
Vortices
246
11.2.2.3
Vortices in Neutral Superfluid and KT Transition
248
11.3
Superconductor-Insulator Transition
249
11.3.1
Rotor Model
249
11.3.2
Strong-and Weak-Coupling Expansions
251
References
253
Ί2
Introduction to Lattice Gauge Theories
255
12.1
Introduction: U(l) and Z2 Lattice Gauge Theories
255
12.1.1
Lattice Gauge Theories
256
12.1.2
Z2 Gauge Theory
260
12.2
Strong- and Weak-Coupling Expansions in U(l) Lattice
Gauge Theory
262
12.2.1
Compactness of Gauge Field and Charge Quantization
264
12.2.2
Charge Confinement
265
12.2.3
Finite 1/g Correction, Loop and String Gas
266
12.2.4
Confinement-to-Plasma Phase Transition and String-Net
Condensation
267
12.3
Instantons
in 2+1D U(l) Lattice Gauge Theory
268
12.3.1
Plasma and Confinement Phases
269
12.3.2
Wilson Loop
272
12.4
Duality Between a Neutral Superfluid and U(l) Gauge Theory Coupled to
Charged Bosons
275
12.4.1
Vortices in Vortex Liquid
277
References
278
Appendix: One-Particle Green s Function in Second-Order
Perturbation Theory
279
Index
285
|
| adam_txt |
vu
Contents
Acknowledgements
V
Introduction
to Classical and Quantum Field Theory
XIII
Part One
1
1
Introduction
3
1.1
What is a Field Theory?
3
1.1.1
Mathematical Description
3
1.2
Basic Mathematical Tools in (Classical) Field Theory
5
1.2.1
Solution of Field Equations of Motion
5
1.2.1.1
Eigenfunction Expansion Method
6
1.2.1.2
Eigenfunction Expansions for Green's Functions
7
1.2.1.3
A Variant of the Above Method: Initial Condition Problem
8
1.2.1.4
Comment on
Non-
Linear Equations of Motion
10
1.2.2
Evaluation of Partition Function for Quadratic Field Theories
10
1.2.2.1
Non-Linear Energy Functional
13
1.2.2.2
Continuum Limit
13
1.2.2.3
Constraints
14
2
Basics of Classical Field Theory
17
2.1
Lagrangian
Formulation
for Classical Mechanics/Field
Theory
17
2.1.1
Basic
Ansatz:
The Principle of Least Action
17
2.1.1.1
Conservation of Energy and Momentum
18
2.1.1.2
Galilean
Invariance
and the Most General Form
of Lagrangian
19
2.1.1.3
Constraints
21
2.1.1.4
Lagrangian Formulation for Classical Field Theory
21
2.1.1.5
Space-Time Symmetric Lagrangian Formulation
23
2.2
Conservation Laws in Continuum Field Theory (Noether's
Theorem)
24
Vili
Contents
2.2.1
Energy-Momentum Conservation
24
2.2.1.1
Internal Symmetry and Noether's Theorem
26
2.2.2
More Complicated Internal Symmetries
27
References
28
3
Quantization of Classical Field Theories (I)
29
3.1
Canonical Quantization of Scalar Fields: Bosonic Systems
29
3.1.1
General Quadratic Hamiltonian and Bosons
31
3.1.2
Interaction Between Particles
33
3.1.3
Continuum Limit of Lattice Field Theory
34
3.2
Introduction to Quantum Statistics
35
3.2.1
Fock Space for Bosons and
Fermions
36
3.2.2
Introduction to
Grassmann
Field and Quantum Field Theory
for
Fermions
38
3.3
Path Integral Quantization of Mechanics and Field Theory
41
3.3.1
Imaginary-Time Path Integral and Partition Function
43
3.3.2
Application to Quantum Field Theory
45
References
47
4
Quantization of Classical Field Theories (II)
49
4.1
Path Integral Quantization in Coherent State Representations
of Bosons and
Fermions
49
4.1.1
Imaginary Time and Partition Function
51
4.1.1.1
Quantum Field Theory for Bosons
51
4.1.1.2
Quantum Field Theory for
Fermions
52
4.2
Two Simple Examples of QFT
54
4.2.1
Phonons
54
4.2.1.1
Continuum Limit
55
4.2.2
Dirac
Fermions
in ID
56
4.2.2.1
Covariant form of Dirac equation
59
4.2.3
Quantization of Dirac Equation
60
4.2.3.1
Lattice Dirac
Fermions
61
4.3
Simple Applications of Path Integral Formulation
63
4.4
Symmetry and Conservation Laws in Quantum Field Theory
67
References
69
Part Two
71
5
Perturbation Theory, Variational Approach and Correlation Functions
73
5.1
Introduction to Perturbation Theory
73
5.1.1
Path Integral Approach
74
5.1.1.1
Perturbation Theory for Interacting Systems
76
5.1.1.2
Wick's Theorem
77
5.1.2
Dyson's Approach
79
5.1.2.1
Time-Evolution Operator at Imaginary Time
81
Contents
IX
5.1.2.2
Perturbation
Expansion
for S Matrix
81
5.1.2.3
Wick's Theorem in Dyson's Approach
83
5.1.2.4
Example: One-Particle Green's Function
84
5.1.2.5
Perturbation Expansion for One-Particle Green's Function
86
5.1.2.6
Spectral Representation
89
5.2
Variational Approach and Perturbation Theory
92
5.2.1
Example: Hartree-Fock Approximation
93
5.3
Some General Properties of Correlation Functions
95
5.3.1
Linear Response Theory
95
5.3.2
Temperature and Causal Correlation Functions
99
5.3.3
Fluctuation-Dissipation Theorem
101
References
105
6
Introduction to Berry Phase and Gauge Theory
107
6.1
Introduction to Berry Phase
207
6.1.1
Berry Phase for a Simple Quantum System
107
6.1.2
Berry Phase and Particle Statistics 111
6.1.3
Berry Phase and U(l) Gauge Theory
112
6.1.3.1
Relation Between
Αμ
and Berry Phase
113
6.1.4
Electromagnetism
as Gauge Theory
114
6.2
Singular Gauge Potentials and Angular Momentum Quantization
116
6.2.1 Aharonov-Bohm (AB)
Effect
116
6.2.2
Alternative Description of the Problem
118
6.2.3
Magnetic
Monopole
and Angular Momentum Quantization
118
6.2.3.1
Geometrical Theory of Angular Momentum
119
6.2.3.2
Berry Phase and Angular Momentum Quantization
121
6.2.3.3
Quantization of Magnetic
Monopole 121
6.2.3.4
Two Dimensions
123
6.2.3.5
Angular Momentum: Statistics Theorem
123
6.3
Quantization of Electromagnetic Field
124
6.3.1
Canonical Quantization
124
6.3.2
Path Integral Quantization
126
6.3.3
Gauge Problem
127
References
128
7
Introduction to Effective Field Theory, Phases, and Phase
Transitions
129
7.1
Introduction to Effective Field Theory: Boltzmann Equation
and Fluid Mechanics
129
7.1.1
Fluid Mechanics
132
7.1.1.1
Friction and Viscosity
134
7.1.1.2
Limitation of Hydrodynamics: An Example
135
7.2
Landau Theory of Phases and Phase Transitions
136
7.2.1
Order Parameters
136
7.2.1.1
Paramagnetic
<-*
Ferromagnetic Transition
137
X
Contents
7.2.1.2 Liquid <-+
Solid Transition
137
7.2.1.3
Phase Transitions and Broken Ergodicity
137
7.2.2
Landau's Phenomenological Theory of Phase Transitions
139
7.2.2.1
Weakly First-Order Phase Transition
141
7.2.2.2
Effective Free Energies in Landau Theory
143
7.2.2.3
Continuum Limit and Landau Theory
145
7.2.2.4
Quantum Phase Transitions
146
7.3
Other Examples of Effective Classical and Quantum
Field Theories
147
7.3.1
Projective
Hubert Space (Mori) Approach and Correlation
Functions
148
7.3.2
Quantum Principle of Least Action and Applications
150
7.3.2.1
Quasi-particles
152
7.3.3
(Generalized)
Langevin
and Fokker-Planck Equations
153
7.3.3.1
Fokker-Planck Equation
156
References
257
8 Solitons,
Instantons,
and Topology in QFT
159
8.1
Introduction to
Solitons 159
8.1.1
Stability of
Solitons
and Topology
162
8.1.1.1
Topological Index for One-Dimensional Scalar Fields
164
8.1.2
Multi-Kink Solutions and Difference Between Solitary
Wave and Soliton
164
8.1.2.1
Quantization of Solitons/Solitary Waves
165
8.2
Introduction to
Instantons
165
8.2.1 Instantons in
ID Classical Theories
165
8.2.1.1 Instantons in
Quantum Mechanics: Quantum
Tunneling
168
8.2.2
Winding Number
169
8.3
Vortices and Kosterlitz-Thouless Transition
171
8.3.1
Low-Temperature Spin-Spin Correlation Function
174
8.3.2
Kosterlitz-Thouless Transition
175
8.3.3
Screening and KT Transition
177
8.3.4
Vortices in Superconductors and
Superfluide
279
8.4
Skyrmions and
Monopoles
280
8.4.1
Spinor (CPi)
Representation
183
8.4.2
Meaning of Gauge Field
284
8.4.3
Magnetic
Monopoles
285
References
186
Part Three A Few Examples
287
9
Simple Boson Liquids: Introduction to Superfluidity
289
9.1
Saddle-Point Approximation: Semiclasskal Theory for
Interacting Bosons
289
Contents
XI
9.1.1 Semidassical Approximation
(using
One-Partide QM
as Example)
189
9.1.2
Density-Density Response Function and One-Particle
Green's Function
296
9.1.2.1
A Little Bit Beyond the Semiclassical Approximation
197
9.2
Superfluidity
198
9.2.1
Bose
Condensation
198
9.2.2
Superfluid He4
199
9.2.3
Landau's Analysis for Superfluidity
199
9.2.3.1
A Free Boson Condensate is Not a Superfluid
202
9.2.3.2
A Boson Fluid with Phonon-Like Excitation Spectrum
is a Superfluid
201
9.2.3.3
Off-Diagonal Long-Range Order (ODLRO) and Collective
Motion of Superfluid
202
9.2.3.4
Two-Fluid Picture
203
9.3
Charged
Superfluide: Higgs
Mechanism and
Superconductivity
204
9.3.1 Goldstone
Theorem and Higgs Mechanism
204
9.3.2
Higgs Mechanism and Superconductivity
207
9.3.2.1
Meissner Effect (Higgs Mechanism on Gauge Field)
207
9.4
Supersolids
208
9.5
A Brief Comment Before Ending
210
References
210
10
Simple Fermion Liquids: Introduction to Fermi Liquid Theory
222
10.1
Single-Partide and Collective Excitations in
Fermi Liquids
222
10.1.1
The Spectrum of a Free Fermi Gas
212
10.1.2
Collective Modes in Fermi Liquid
213
10.1.2.1
Hubbard-Stratonovich Transformation
214
10.1.2.2
Excitation
Speerram
of Electron Gas in
RPA
218
10.1.3
Alternative Derivation for
RPA
229
10.1.4
Screening
221
10.2
Introduction to Fermi liquids and Fermi Liquid Theory
222
10.2.1
Quasi-partides and Single-Partide Green's Function
224
10.2.2
Charge and Current Carried by Quasi-particles
225
10.2.3
Two Examples of Applications
227
10.2.4
Bosonization Description of Fermi Liquid Theory
229
10.2.5
Beyond Fermi liquid Theory?
230
References
232
11
Superconductivity: BCS Theory and Beyond
233
11.1
BCS Theory for (s-wave) Superconductors: Path Integral
Approach
233
11.1.1
Semiclassical (Gaussian) Theory
237
XII Contents
11.2
BCS
Theory for (s-Wave) Superconductors: Fermion
Excitations and Hamiltonian Approach
239
11.2.1
Variational Waveftmction in BCS Theory
241
11.2.2
GL Equation and Vortex Solution
242
11.2.2.1
Flux Quantization
244
11.2.2.2
Vortices
246
11.2.2.3
Vortices in Neutral Superfluid and KT Transition
248
11.3
Superconductor-Insulator Transition
249
11.3.1
Rotor Model
249
11.3.2
Strong-and Weak-Coupling Expansions
251
References
253
Ί2
Introduction to Lattice Gauge Theories
255
12.1
Introduction: U(l) and Z2 Lattice Gauge Theories
255
12.1.1
Lattice Gauge Theories
256
12.1.2
Z2 Gauge Theory
260
12.2
Strong- and Weak-Coupling Expansions in U(l) Lattice
Gauge Theory
262
12.2.1
Compactness of Gauge Field and Charge Quantization
264
12.2.2
Charge Confinement
265
12.2.3
Finite 1/g Correction, Loop and String Gas
266
12.2.4
Confinement-to-Plasma Phase Transition and String-Net
Condensation
267
12.3
Instantons
in 2+1D U(l) Lattice Gauge Theory
268
12.3.1
Plasma and Confinement Phases
269
12.3.2
Wilson Loop
272
12.4
Duality Between a Neutral Superfluid and U(l) Gauge Theory Coupled to
Charged Bosons
275
12.4.1
'Vortices' in Vortex Liquid
277
References
278
Appendix: One-Particle Green's Function in Second-Order
Perturbation Theory
279
Index
285 |
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| indexdate | 2024-07-09T21:20:43Z |
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| isbn | 9783527407262 |
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| spelling | Ng, Tai-Kai Verfasser aut Introduction to classical and quantum field theory Tai-Kai Ng Weinheim Wiley-VCH 2009 XIV, 292 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Physics textbook Feldtheorie - Lehrbuch Condensed matter Problems, exercises, etc Condensed matter Textbooks Quantum field theory Problems, exercises, etc Quantum field theory Textbooks Quantenfeldtheorie (DE-588)4047984-5 gnd rswk-swf Feldtheorie (DE-588)4016698-3 gnd rswk-swf (DE-588)4123623-3 Lehrbuch gnd-content Feldtheorie (DE-588)4016698-3 s DE-604 Quantenfeldtheorie (DE-588)4047984-5 s Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016705040&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Ng, Tai-Kai Introduction to classical and quantum field theory Feldtheorie - Lehrbuch Condensed matter Problems, exercises, etc Condensed matter Textbooks Quantum field theory Problems, exercises, etc Quantum field theory Textbooks Quantenfeldtheorie (DE-588)4047984-5 gnd Feldtheorie (DE-588)4016698-3 gnd |
| subject_GND | (DE-588)4047984-5 (DE-588)4016698-3 (DE-588)4123623-3 |
| title | Introduction to classical and quantum field theory |
| title_auth | Introduction to classical and quantum field theory |
| title_exact_search | Introduction to classical and quantum field theory |
| title_exact_search_txtP | Introduction to classical and quantum field theory |
| title_full | Introduction to classical and quantum field theory Tai-Kai Ng |
| title_fullStr | Introduction to classical and quantum field theory Tai-Kai Ng |
| title_full_unstemmed | Introduction to classical and quantum field theory Tai-Kai Ng |
| title_short | Introduction to classical and quantum field theory |
| title_sort | introduction to classical and quantum field theory |
| topic | Feldtheorie - Lehrbuch Condensed matter Problems, exercises, etc Condensed matter Textbooks Quantum field theory Problems, exercises, etc Quantum field theory Textbooks Quantenfeldtheorie (DE-588)4047984-5 gnd Feldtheorie (DE-588)4016698-3 gnd |
| topic_facet | Feldtheorie - Lehrbuch Condensed matter Problems, exercises, etc Condensed matter Textbooks Quantum field theory Problems, exercises, etc Quantum field theory Textbooks Quantenfeldtheorie Feldtheorie Lehrbuch |
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