24小时热门版块排行榜

返回列表

【奖励】本帖被评价8次，作者pkusiyuan增加金币 6.4 个

pkusiyuan

银虫 (正式写手)

应助: 0 (幼儿园)
金币: 15204.9
帖子: 773
在线: 130小时
虫号: 3451204

[资源] De Gruyter2012Theory of Interacting Quantum Fields

Contents
Preface v
Notation viii
0 Introduction 1
I Symmetry Groups of Elementary Particles
1 Lorentz Group 8
1.1 Euclidean and Minkowski Spaces. Relativistic Notation . . . . . . . 8
1.2 HomogeneousLorentzGroup . . . . . . . . . . . . . . . . . . . . . 11
1.3 Inhomogeneous Lorentz Group–Poincaré Group . . . . . . . . . . . 14
1.4 ComplexLorentzTransformations . . . . . . . . . . . . . . . . . . 15
1.5 Representations of the Lorentz and Poincaré Groups, Field Functions,
and Physical States . . . . . . . . . . . . . . . . . . . . . . . . . . 16
1.5.1 Representation D.0;0/ . . . . . . . . . . . . . . . . . . . . 19
1.5.2 Representations D. 1
2 ;0/ and D.0; 1
2 / . . . . . . . . . . . . . 20
1.5.3 Representation D. 1
2 ; 1
2 / . . . . . . . . . . . . . . . . . . . . 20
2 Groups of Internal Symmetries 23
2.1 Abelian Unitary Group U.1/ . . . . . . . . . . . . . . . . . . . . . 23
2.2 Charge Conjugation C . . . . . . . . . . . . . . . . . . . . . . . . 24
2.3 Special Unitary Group SU.n/ . . . . . . . . . . . . . . . . . . . . 24
2.3.1 SU.2/Symmetry . . . . . . . . . . . . . . . . . . . . . . . 25
2.3.2 SU.3/Symmetry . . . . . . . . . . . . . . . . . . . . . . . 27
2.4 Groups of Local Transformations. Gauge Group . . . . . . . . . . . 29
3 Problems to Part I 35
II Classical Theory of the Free Fields
4 Lagrangian and Hamiltonian Formalisms
of the Classical Field Theory 39
4.1 Variational Principle and Canonical Formalism
of Classical Mechanics . . . . . . . . . . . . . . . . . . . . . . . . 39
4.1.1 LagrangianEquations . . . . . . . . . . . . . . . . . . . . 39
xii Contents
4.1.2 Canonical Variables. Hamiltonian Equations . . . . . . . . 41
4.1.3 PoissonBrackets. Integrals ofMotion . . . . . . . . . . . . 42
4.1.4 Canonical Formalism in the Presence of Constraints . . . . 43
4.2 From Classical to Quantum Mechanics. Primary Quantization . . . 48
4.3 General Requirements to the Lagrangians of the Field Theory . . . . 52
4.4 Lagrange–EulerEquations . . . . . . . . . . . . . . . . . . . . . . 53
4.5 Noether’sTheoremandDynamic Invariants . . . . . . . . . . . . . 54
4.6 Vector of Energy-Momentum . . . . . . . . . . . . . . . . . . . . . 56
4.7 Tensors ofAngularMomentumandSpin . . . . . . . . . . . . . . . 57
4.8 Charge and the Vector of Current . . . . . . . . . . . . . . . . . . . 59
4.9 Canonical Variables . . . . . . . . . . . . . . . . . . . . . . . . . . 60
5 Classical Theory of Free Scalar Fields 61
5.1 Klein–Fock–Gordon Equation . . . . . . . . . . . . . . . . . . . . 61
5.2 Relativistic Invariance of the Klein–Fock–Gordon Equation . . . . . 62
5.3 Solutions of the Klein–Fock–Gordon Equation . . . . . . . . . . . . 64
5.4 Interpretation of Solutions. Hilbert Space of States . . . . . . . . . 66
5.5 bC, bP, and bT Transformations . . . . . . . . . . . . . . . . . . . . . 70
5.5.1 Transformation of Charge Conjugation bC . . . . . . . . . . 70
5.5.2 Space Reflection bP . . . . . . . . . . . . . . . . . . . . . . 72
5.5.3 Time Reversal bT . . . . . . . . . . . . . . . . . . . . . . . 73
5.5.4 bC bPbT-Invariance . . . . . . . . . . . . . . . . . . . . . . . 73
5.6 Representations of the Lorentz Group in the Space of States . . . . . 74
5.7 Lagrangian Formalism of the Scalar Field. Dynamic Invariants . . . 78
6 Spinor Field 82
6.1 Dirac Equation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82
6.1.1 Construction of the Dirac Equation . . . . . . . . . . . . . 82
6.1.2 Properties of Dirac Matrices. Conjugate Equation . . . . . . 83
6.2 Relativistic Invariance . . . . . . . . . . . . . . . . . . . . . . . . . 86
6.2.1 Transformation Properties of the Spinor Field . . . . . . . . 87
6.2.2 On Reducible and Irreducible Spinor Representations . . . . 91
6.2.3 Transformation Properties of Bilinear Forms NO . . . . . 92
6.3 Solutions of the Dirac Equation . . . . . . . . . . . . . . . . . . . . 94
6.3.1 Structure ofSolutions in theMomentumSpace . . . . . . . 94
6.3.2 Classification of Solutions. Helicity . . . . . . . . . . . . . 97
6.3.3 Relations Between Spinors . . . . . . . . . . . . . . . . . . 102
6.3.4 Wave Functions of the Electron and Positron.
Charge Conjugation . . . . . . . . . . . . . . . . . . . . . 104
Contents xiii
6.3.5 bC bPbT -Transformation . . . . . . . . . . . . . . . . . . . . 107
6.4 Lagrangian Formalism . . . . . . . . . . . . . . . . . . . . . . . . 110
6.5 Representations of the Lorentz Group . . . . . . . . . . . . . . . . 115
6.5.1 Hilbert Space of States . . . . . . . . . . . . . . . . . . . . 115
6.5.2 Representations of the Lorentz Group in the Space of States 117
6.6 Applications of the Dirac Equation . . . . . . . . . . . . . . . . . . 118
6.6.1 Dirac Equation in the Presence of External Fields . . . . . . 118
6.7 Massless Spinor Field . . . . . . . . . . . . . . . . . . . . . . . . . 121
6.7.1 Two-component Massless Spinor Field . . . . . . . . . . . 121
6.7.2 Relativistic Invariance . . . . . . . . . . . . . . . . . . . . 123
6.7.3 Are There Actual Particles Corresponding to the
Massless Spinor Fields? Physical Interpretation
ofSolutions. Neutrino . . . . . . . . . . . . . . . . . . . . 123
6.7.4 Lagrangian andDynamic Invariants . . . . . . . . . . . . . 125
6.7.5 On theMass ofNeutrino andMajoranaSpinors . . . . . . . 126
7 Vector Fields 128
7.1 Lagrangian Formalism . . . . . . . . . . . . . . . . . . . . . . . . 128
7.2 Representations in the Momentum Space . . . . . . . . . . . . . . . 131
7.3 Decomposition into the Longitudinal and Transverse Components . 131
7.4 bP;bT ; bC-Transformations . . . . . . . . . . . . . . . . . . . . . . . 133
8 Electromagnetic Field 135
8.1 MaxwellEquations . . . . . . . . . . . . . . . . . . . . . . . . . . 135
8.2 Potential of the Electromagnetic Field . . . . . . . . . . . . . . . . 136
8.3 Gradient Transformations and the Lorentz Condition: Transversality
Condition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137
8.4 Lagrangian Formalism for Electromagnetic Fields . . . . . . . . . . 139
8.5 Transversal, Longitudinal, and Time Components
of the Electromagnetic Field . . . . . . . . . . . . . . . . . . . . . 141
8.6 Quantum-Mechanical Characteristics of Photons . . . . . . . . . . . 143
8.7 bC; bP;bT-Transformations . . . . . . . . . . . . . . . . . . . . . . . 146
8.8 Consistency of the Lorentz and Gauge Transformations.
VariousTypes ofGauges . . . . . . . . . . . . . . . . . . . . . . . 146
9 Equations for Fields with Higher Spins 149
9.1 Fields with Spin 3=2 . . . . . . . . . . . . . . . . . . . . . . . . . 149
9.2 Particles with Spin 2 . . . . . . . . . . . . . . . . . . . . . . . . . 151
10 Problems to Part II 152
xiv Contents
III Classical Theory of Interacting Fields
11 Gauge Theory of the Electromagnetic Interaction 158
11.1 Principle ofGauge Invariance in theMaxwellTheory . . . . . . . . 158
11.2 Schrödinger Equation and Gradient (Gauge) Invariance . . . . . . . 159
11.3 Gauge Principle as the Dynamical Principle of Interaction between
the Electromagnetic and Electron-Positron Fields . . . . . . . . . . 161
12 Classical Theory of Yang–Mills Fields 164
12.1 Gauge Principle and the Lagrangian of the Yang–Mills Fields . . . . 164
12.2 Equations of Motion for the Free Yang–Mills fields . . . . . . . . . 167
12.3 Yang–Mills Fields for Arbitrary Representations
of the Group SU.N/ . . . . . . . . . . . . . . . . . . . . . . . . . 169
13 Masses of Particles and Spontaneous Breaking of Symmetry 171
13.1 SpontaneousBreaking ofSymmetry . . . . . . . . . . . . . . . . . 172
13.2 Higgs Mechanism for the Local U.1/Symmetry . . . . . . . . . . . 174
13.3 Higgs Mechanism for the Local SU.2/ symmetry . . . . . . . . . . 176
13.4 Generation of the Masses of Fermions . . . . . . . . . . . . . . . . 179
14 On the Construction of the General Lagrangian of Interacting Fields 181
14.1 Lagrangian of theQCD . . . . . . . . . . . . . . . . . . . . . . . . 183
14.2 Lagrangian of Weak Interactions . . . . . . . . . . . . . . . . . . . 184
14.3 On the Electroweak Interactions . . . . . . . . . . . . . . . . . . . 188
14.4 On the Lagrangian of Great Unification . . . . . . . . . . . . . . . 189
15 Solutions of the Equations for Classical Fields: Solitary Waves,
Solitons, Instantons 191
16 Problems to Part III 197
IV Second Quantization of Fields
17 Axioms and General Principles of Quantization 201
17.1 Why Do We Need the Procedure of Second Quantization? Operator
Nature of the Field Functions . . . . . . . . . . . . . . . . . . . . . 201
17.2 Schrödinger, Heisenberg, and Interaction Pictures . . . . . . . . . . 202
17.3 Axioms of Quantization . . . . . . . . . . . . . . . . . . . . . . . . 204
17.4 Relativistic Heisenberg Equation for Quantized Fields . . . . . . . . 213
17.4.1 Heisenberg Equation for a Free Scalar Field . . . . . . . . . 214
17.4.2 Heisenberg Equation for a Free Electron-Positron Field . . . 215
Contents xv
17.5 Physical Content of Positive- and Negative-Frequency Solutions of
Equations for Free-Field Operators . . . . . . . . . . . . . . . . . . 217
18 Quantization of the Free Scalar Field 218
18.1 Commutation Relations. Commutator Functions . . . . . . . . . . . 218
18.2 Complex Scalar Field . . . . . . . . . . . . . . . . . . . . . . . . . 220
18.3 Operator Relations for Dynamic Invariants . . . . . . . . . . . . . . 221
19 Quantization of the Free Spinor Field 222
19.1 Commutator Functions of Fermi Fields . . . . . . . . . . . . . . . . 222
19.2 Dynamic Invariants of a Free Spinor Field . . . . . . . . . . . . . . 224
20 Quantization of the Vector and Electromagnetic Fields. Specific
Features of the Quantization of Gauge Fields 225
20.1 Quantization of the Complex Vector Field . . . . . . . . . . . . . . 225
20.2 Quantization of an Electromagnetic Field . . . . . . . . . . . . . . 229
20.2.1 Specific Features and Difficulties of the Quantization of an
Electromagnetic Field . . . . . . . . . . . . . . . . . . . . 229
20.2.2 Gupta–Bleuler Formalism . . . . . . . . . . . . . . . . . . 232
20.2.3 Canonical Method of Quantization . . . . . . . . . . . . . . 236
20.3 On the Quantization of Gauge Fields . . . . . . . . . . . . . . . . . 238
21 CPT . Spin and Statistics 240
21.1 The Transformation of Charge Conjugation . . . . . . . . . . . . . 241
21.2 The Transformation of Space Reflection . . . . . . . . . . . . . . . 242
21.3 The Transformation of Time Reversal . . . . . . . . . . . . . . . . 243
21.4 CPT -Theorem and the Connection of Spin and Statistics . . . . . . 246
21.5 Proofof thePauliTheorem . . . . . . . . . . . . . . . . . . . . . . 248
22 Representations of Commutation and Anticommutation Relations 250
22.1 GeneralStructure of theFockSpace . . . . . . . . . . . . . . . . . 250
22.2 Representations of Commutation Relations for a Free Real
Scalar Field . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 252
22.2.1 The Fock Space of Free Scalar Bosons . . . . . . . . . . . . 252
22.2.2 Operators of Creation and Annihilation in the Fock Space.
Momentum Representation . . . . . . . . . . . . . . . . . . 252
22.2.3 Vacuum State of Free Particle. Cyclicity of Vacuum. Set of
Exponential Vectors . . . . . . . . . . . . . . . . . . . . . 256
22.2.4 Construction of Representations of Commutation Relations
for a Complex Scalar Field . . . . . . . . . . . . . . . . . . 259
xvi Contents
22.2.5 Construction of Representations of Commutation Relations
in the Configuration Space. Relativistic Invariance of
a Free Field . . . . . . . . . . . . . . . . . . . . . . . . . . 260
22.3 Representation of Anticommutation Relations of Spinor Fields . . . 262
22.3.1 Representation of Anticommutation Relations of the
Operators of Creation and Annihilation of Fermions and
Antifermions . . . . . . . . . . . . . . . . . . . . . . . . . 262
22.3.2 Representation of Anticommutation Relations in the
Configuration Space . . . . . . . . . . . . . . . . . . . . . 265
22.4 Space of States of a Free Electromagnetic Field . . . . . . . . . . . 267
22.5 Space of Occupation Numbers . . . . . . . . . . . . . . . . . . . . 271
23 Green Functions 274
23.1 Green Functions of the Scalar Field . . . . . . . . . . . . . . . . . 274
23.2 The Green Functions of Spinor, Vector, and Electromagnetic Fields . 277
23.3 Time-Ordered Product and Green Functions . . . . . . . . . . . . . 278
23.4 WickTheorems . . . . . . . . . . . . . . . . . . . . . . . . . . . . 279
23.4.1 WickTheoremforNormalProducts . . . . . . . . . . . . . 279
23.4.2 Wick Theorem for a Time-Ordered Product . . . . . . . . . 281
23.4.3 Generalized Wick Theorem . . . . . . . . . . . . . . . . . 284
23.5 Operation of Multiplication and the Regularization of Distributions . 284
23.6 N-Point Green Functions of Free Fields . . . . . . . . . . . . . . . 285
24 Problems to Part IV 287
V Quantum Theory of Interacting Fields. General Problems
25 Construction of Quantum Interacting Fields and Problems
of This Construction 291
25.1 Formal Construction of a Quantum Field . . . . . . . . . . . . . . . 291
25.2 Mathematical Problems of Construction of a Quantum
Interacting Field . . . . . . . . . . . . . . . . . . . . . . . . . . . . 294
26 Scattering Theory. Scattering Matrix 298
26.1 Quantum Description of Scattering. Definition of Scattering
Operator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 298
26.2 Formal Construction of the Scattering Operator by the Method
of Perturbation Theory . . . . . . . . . . . . . . . . . . . . . . . . 302
26.3 Main Properties of the S-Operator . . . . . . . . . . . . . . . . . . 305
26.3.1 Normal Form of the Operator S . . . . . . . . . . . . . . . 305
26.3.2 Invariance of the Scattering Matrix under Lorentz
Transformations and Transformations of Charge Conjugation 309
Contents xvii
26.3.3 Unitarity of the Scattering Operator . . . . . . . . . . . . . 310
26.3.4 Law of Conservation of Energy . . . . . . . . . . . . . . . 311
26.3.5 Matrix Elements of the S-Operator and the Scattering
Amplitude . . . . . . . . . . . . . . . . . . . . . . . . . . . 313
26.4 FeynmanDiagrams . . . . . . . . . . . . . . . . . . . . . . . . . . 316
26.4.1 Feynman Diagrams for the S-Operator . . . . . . . . . . . 317
26.4.2 Feynman Diagrams for Coefficient Functions
of the S-Operator . . . . . . . . . . . . . . . . . . . . . . . 317
26.4.3 Feynman Diagrams for Matrix Elements of the S-Operator . 319
26.5 Effective Cross-Sections and Scattering Matrix . . . . . . . . . . . 322
26.5.1 Classical Picture . . . . . . . . . . . . . . . . . . . . . . . 323
26.5.2 Quantum Picture . . . . . . . . . . . . . . . . . . . . . . . 325
27 Equations for Coefficient Functions of the S-Matrix 327
27.1 Creation and Annihilation Operators of External Lines of Feynman
Diagrams . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 328
27.2 Equations of theResolventType . . . . . . . . . . . . . . . . . . . 331
27.3 Equations of theEvolutionType . . . . . . . . . . . . . . . . . . . 334
28 Green Functions and Scattering Matrix 336
28.1 Green Functions and the S-Matrix in the Interaction Picture . . . . . 336
28.2 Schwinger Equation for Green Functions . . . . . . . . . . . . . . . 338
28.3 On the Relationship between the Green Functions and the Coefficient
Functions of the Scattering S-Operator . . . . . . . . . . . . . . . . 341
28.4 Equations for Green Functions in Terms of Functional Derivatives . 342
28.5 Equations for Truncated Green Functions . . . . . . . . . . . . . . 344
28.6 Equations for One-Particle Irreducible Green Functions.
Dyson Equation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 347
28.7 Spectral Representation of the 2-Point Green Function
(Källén–Lehmann Representation) . . . . . . . . . . . . . . . . . . 353
29 On Renormalization in Perturbation Theory 358
29.1 Primitively-Divergent Diagrams. Separation of Divergences by the
Pauli–Villars Method . . . . . . . . . . . . . . . . . . . . . . . . . 358
29.2 Degree ofDivergence ofFeynmanDiagram . . . . . . . . . . . . . 365
29.3 Elimination of Divergences by the Method of Bogoliubov–Parasiuk
R-Operation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 368
29.4 R-Operation and Counterterms of a Lagrangian . . . . . . . . . . . 374
29.5 Classification of Interactions: Renormalizable and
Nonrenormalizable Theories . . . . . . . . . . . . . . . . . . . . . 379
xviii Contents
29.6 Relationship between Counterterms and the Renormalization of Main
Constants of theTheory . . . . . . . . . . . . . . . . . . . . . . . . 380
29.7 Equivalent Types of Renormalizations . . . . . . . . . . . . . . . . 387
30 Method of Functional (Path) Integrals in Quantized Field Theory 391
30.1 Notion of Path Integration and Main Formulas . . . . . . . . . . . . 392
30.2 Formalism of Feynman Integrals (Path Integrals) in Quantum
Mechanics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 400
30.3 Formalism of Feynman Integrals for Systems with Constraints . . . 405
30.4 Path Integral Representation for Scalar Fields . . . . . . . . . . . . 409
30.5 Path Integral Representation for Fermi Fields . . . . . . . . . . . . 411
31 Problems to Part V 416
VI Axiomatic and Euclidean Field Theories
32 Wightman Axiomatics 423
32.1 Wightman Axioms for Real Scalar Fields . . . . . . . . . . . . . . 423
32.2 Wightman Functions and Their Properties . . . . . . . . . . . . . . 425
32.3 Reconstruction Theorem . . . . . . . . . . . . . . . . . . . . . . . 427
33 Other Axiomatic Approaches 429
33.1 Haag–Ruelle Scattering Theory (HRST) . . . . . . . . . . . . . . . 429
33.2 Lehmann–Symanzik–Zimmermann Axiomatics . . . . . . . . . . . 432
33.3 Bogoliubov–Medvedev–Polivanov (BMP) Axiomatic Approach . . 435
34 Euclidean Field Theory 439
34.1 Analytic Continuation of Feynman Amplitudes . . . . . . . . . . . 440
34.2 Operators of Free Euclidean Fields . . . . . . . . . . . . . . . . . . 442
34.2.1 Real scalar field . . . . . . . . . . . . . . . . . . . . . . . . 442
34.2.2 Euclidean Fermi fields . . . . . . . . . . . . . . . . . . . . 444
34.3 Euclidean Green Functions of a Free Scalar Field . . . . . . . . . . 446
34.4 Euclidean Green Functions of Interacting Fields . . . . . . . . . . . 447
35 Euclidean Axiomatics 453
35.1 Analytic Continuation of Generalized Wightman Functions . . . . . 453
35.2 Euclidean Green Functions. Osterwalder–Schrader Axioms . . . . . 455
35.3 Reconstruction of the Wightman Theory . . . . . . . . . . . . . . . 457
36 Problems to Part VI 460
Contents xix
VII Quantum Theory of Gauge Fields
37 Quantum Electrodynamics (QED) 465
37.1 Quantization of Interacting Electromagnetic Fields . . . . . . . . . 466
37.1.1 Gupta–Bleuler Formalism for Interacting
Electromagnetic Fields . . . . . . . . . . . . . . . . . . . . 466
37.1.2 Quantization of Interacting Electromagnetic Fields
in theCoulombGauge . . . . . . . . . . . . . . . . . . . . 467
37.1.3 PhotonPropagator andGaugeConditions . . . . . . . . . . 469
37.2 S-Matrix inQED . . . . . . . . . . . . . . . . . . . . . . . . . . . 471
37.2.1 Perturbation Theory. Feynman Diagrams . . . . . . . . . . 471
37.2.2 Coefficient Functions of the S-Matrix in Terms of Creation
and Annihilation Operators of Lines of Feynman Diagrams . 474
37.2.3 FurryTheorem . . . . . . . . . . . . . . . . . . . . . . . . 476
37.2.4 Gauge Invariance for Coefficient Functions of the
S-Operator . . . . . . . . . . . . . . . . . . . . . . . . . . 479
37.3 Equations for Green Functions and Coefficient Functions of the
S-Matrix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 480
37.3.1 Schwinger Equation . . . . . . . . . . . . . . . . . . . . . 480
37.3.2 System of Equations for Self-Energy and Vertex Parts
ofGreenFunctions . . . . . . . . . . . . . . . . . . . . . . 482
37.4 Divergences in QED and Methods for Their Elimination . . . . . . 485
37.4.1 Primitively-Divergent Diagrams and Their Regularization . 485
37.4.2 Mass and Charge Renormalization of Electron (Positron) . . 490
37.5 Spectral Representations of 2-Point Green Functions . . . . . . . . 493
38 Quantization of Gauge Fields 498
38.1 Path Integral for Green Functions in QED (Coulomb Gauge) . . . . 499
38.2 Covariant Gauges: Popov–Faddeev–de Witt Method . . . . . . . . . 502
38.3 Covariant Quantization of Electromagnetic Interaction . . . . . . . 506
38.3.1 Connection between Different Gauges . . . . . . . . . . . . 507
38.3.2 Ward Identity . . . . . . . . . . . . . . . . . . . . . . . . . 508
38.4 Quantization of Yang–Mills Fields Interacting with Matter Fields . . 510
38.5 Faddeev–PopovGhosts . . . . . . . . . . . . . . . . . . . . . . . . 514
38.6 BRST-Invariance . . . . . . . . . . . . . . . . . . . . . . . . . . . 516
39 Standard Models of Interactions 521
39.1 Renormalization of Gauge Theories . . . . . . . . . . . . . . . . . 521
39.2 On the Masses of Gluons and Spontaneous Symmetry Breakdown . 530
39.2.1 Connection of the Radius of Interaction and the Mass of
ExchangeBosons . . . . . . . . . . . . . . . . . . . . . . . 530
xx Contents
39.2.2 Are Theories with Nonzero Mass of Exchange Bosons
Renormalizable? . . . . . . . . . . . . . . . . . . . . . . . 532
39.2.3 Spontaneous Breakdown of the U.1/-Symmetry . . . . . . . 533
39.2.4 Spontaneous Breakdown of the Local SU.N/-Symmetry . . 535
39.3 Models of Interactions of Elementary Particles . . . . . . . . . . . . 537
39.3.1 Strong Interaction. Model of QCD . . . . . . . . . . . . . . 537
39.3.2 Weak and Electroweak Interactions . . . . . . . . . . . . . 539
40 Problems to Part VII 542
Appendix Hints for the Solution of Problems 544
Bibliography 549
Index 562

回复此楼

» 本帖附件资源列表

欢迎监督和反馈：小木虫仅提供交流平台，不对该内容负责。
本内容由用户自主发布，如果其内容涉及到知识产权问题，其责任在于用户本人，如对版权有异议，请联系邮箱：xiaomuchong@tal.com
附件 1 : Theory_of_Interacting_Quantum_Fields,_Alexei_L._Rebenko,_2012.pdf

2015-03-04 17:18:12, 2.17 M