Quantum Field Theory: By Academician Prof. Kazuhiko Nishijima - A Classic in Theoretical Physics

Foreword
Preface to the English Edition
Preface of the Author
Contents
1 Elementary Particle Theory and Field Theory
1.1 Classification of Interactions and Yukawa's Theory
1.2 The Muon as the First Member of the Second Generation
1.3 Quantum Electrodynamics
1.4 The Road from Pions to Hadrons
1.5 Strange Particles as Members of the Second Generation
1.6 Non-conservation of Parity
1.7 Second Generation Neutrinos
1.8 Democratic and Aristocratic Hadrons—The Quark Model
2 Canonical Formalism and Quantum Mechanics
2.1 Schrödinger's Picture and Heisenberg's Picture
2.2 Hamilton's Principle
2.3 Equivalence Between the Canonical Equations and Lagrange's Equations
2.4 Equal-Time Canonical Commutation Relations
3 Quantization of Free Fields
3.1 Field Theory Based on Canonical Formalism
3.1.1 Canonical Commutation Relations
3.1.2 Euler–Lagrange Equations
Example: Klein–Gordon Equation
3.1.3 Hamiltonian
Example: Hamiltonian for Real Scalar Field
3.2 Relativistic Generalization of the Canonical Equations
3.3 Quantization of the Real Scalar Field
3.4 Quantization of the Complex Scalar Field
3.5 Dirac Equation
3.6 Relativistic Transformations of Dirac's Wave Function
3.7 Solutions of the Free Dirac Equation
3.8 Quantization of the Dirac Field
3.9 Charge Conjugation
3.10 Quantization of the Complex Vector Field
4 Invariant Functions and Quantization of Free Fields
4.1 Unequal-Time Commutation Relations for Real Scalar Fields
4.2 Various Invariant Functions
4.3 Unequal-Time Commutation Relations of Free Fields
4.4 Generalities of the Quantization of Free Fields
5 Indefinite Metric and the Electromagnetic Field
5.1 Indefinite Metric
5.2 Generalized Eigenstates
5.3 Free Electromagnetic Field in the Fermi Gauge
5.4 Lorenz Condition and Physical State Space
5.5 Free Electromagnetic Field: Generalization of Gauge Choices
6 Quantization of Interacting Systems
6.1 Tomonaga–Schwinger Equation
6.2 Retarded Product Expansion of the Heisenberg Operators
6.3 Yang–Feldman Expansion of the Heisenberg Operators
6.4 Examples of Interactions
7 Symmetries and Conservation Laws
7.1 Noether's Theorem for Point-Particle Systems
7.2 Noether's Theorem in Field Theory
7.3 Applications of Noether's Theorem
7.4 Poincaré Invariance
7.5 Representations of the Lorentz Group
7.6 Spin of a Massless Particle
7.7 Pauli–Gürsey Group
8 S-Matrix
8.1 Definition of the S-Matrix
8.2 Dyson's Formula for the S-Matrix
8.3 Wick's Theorem
8.4 Feynman Diagrams
8.5 Examples of S-Matrix Elements
8.5.1 Compton Scattering
8.5.2 Pion Decay to Muons
Two-Photon Decay of 0
8.6 Furry's Theorem
8.7 Two-Photon Decays of Neutral Mesons
9 Cross-Sections and Decay Widths
9.1 Møller's Formulas
9.2 Examples of Cross-Sections and Decay Widths
9.3 Inclusive Reactions
9.4 Optical Theorem
9.5 Three-Body Decays
10 Discrete Symmetries
10.1 Symmetries and Unitary Transformations
10.2 Parity of Antiparticles
10.3 Isospin Parity and G-Conjugation
10.4 Antiunitary Transformations
10.5 CPT Theorem
11 Green's Functions
11.1 Gell-Mann–Low Relation
11.2 Green's Functions and Their Generating Functionals
11.3 Different Time-Orderings in the Lagrangian Formalism
11.4 Matthews' Theorem
11.5 Example of Matthews' Theorem with Modification
11.6 Reduction Formula in the Interaction Picture
11.7 Asymptotic Conditions
11.8 Unitarity Condition on the Green's Function
11.9 Retarded Green's Functions
12 Renormalization Theory
12.1 Lippmann–Schwinger Equation
12.2 Renormalized Interaction Picture
12.3 Mass Renormalization
12.4 Renormalization of Field Operators
12.5 Renormalized Propagators
12.6 Renormalization of Vertex Functions
12.7 Ward–Takahashi Identity
12.8 Integral Representation of the Propagator
12.8.1 Integral Representation
12.8.2 Self-Energy
12.8.3 Integral Representation of the Electromagnetic Field Propagator
12.8.4 Goto–Imamura–Schwinger Term
13 Classification of Hadrons and Models
13.1 Unitary Groups
13.1.1 Representations of a Group
13.1.2 Direct Product Representation
13.1.3 Lie Groups
13.1.4 Orthogonal Group O(n)
13.1.5 Unitary Group U(n)
13.1.6 Special Unitary Group SU(2)
13.2 The Group SU(3)
13.2.1 Generators of SU(3)
13.2.2 I-, U-, and V-Spin
13.2.3 Three-Body Quark Systems
13.2.4 Mass Formulas
13.2.5 Baryon Magnetic Moments
13.2.6 SU(3)-Invariant Interactions
13.2.7 Casimir Operator
13.3 Universality of -Meson Decay Interactions
13.4 Beta-Decay
13.5 Universality of the Fermi Interaction
13.6 Quark Model in Weak Interactions
13.7 Quark Model in Strong Interactions
13.7.1 Mass Formula
13.7.2 Magnetic Moments
13.8 Parton Model
14 What Is Gauge Theory?
14.1 Gauge Transformations of the Electromagnetic Field
14.2 Non-Abelian Gauge Fields
14.3 Gravitational Field as a Gauge Field
15 Spontaneous Symmetry Breaking
15.1 Nambu–Goldstone Particles
15.2 Sigma Model
15.3 The Mechanism of Spontaneous Symmetry Breaking
15.4 Higgs Mechanism
15.5 Higgs Mechanism with Covariant Gauge Condition
15.6 Kibble's Theorem
15.6.1 Adjoint Representation
15.6.2 Kibble's Theorem
16 Weinberg–Salam Model
16.1 Weinberg–Salam Model
16.2 Introducing Fermions
16.3 GIM Mechanism
16.4 Anomalous Terms and Generation of Fermions
16.5 Grand Unified Theory
17 Path-Integral Quantization Method
17.1 Quantization of a Point-Particle System
17.2 Quantization of Fields
18 Quantization of Gauge Fields Using the Path-Integral Method
18.1 Quantization of Gauge Fields
18.1.1 A Method to Specify the Gauge Condition
18.1.2 The Additional Term Method
18.2 Quantization of the Electromagnetic Field
18.2.1 Specifying the Gauge Condition
18.2.2 The Additional Term Method
18.2.3 Ward–Takahashi Identity
18.2.4 Gauge Transformations for Green's Functions
18.3 Quantization of Non-Abelian Gauge Fields
18.3.1 A Method to Specify the Gauge Condition
18.3.2 The Additional Term Method
18.3.3 Hermitization of the Lagrangian Density
18.3.4 Gauge Transformations of Green's Functions
18.4 Axial Gauge
18.5 Feynman Rules in the α-Gauge
19 Becchi–Rouet–Stora Transformations
19.1 BRS Transformations
19.2 BRS Charge
19.3 Another BRS Transformation
19.4 BRS Identity and Slavnov–Taylor Identity
19.5 Representations of the BRS Algebra
19.6 Unitarity of the S-Matrix
19.7 Representations of the Extended BRS Algebra
19.8 Representations of BRS Transformations for Auxiliary Fields
19.9 Representations of BRSNO Algebras
20 Renormalization Group
20.1 Renormalization Group for QED
20.2 Approximate Equations for the Renormalization Group
20.2.1 Approximation Neglecting Vacuum Polarization
20.2.2 Approximation Taking into Account Vacuum Polarization
20.3 Ovsianikov's Equation
20.4 Linear Equations for the Renormalization Group
20.5 Callan–Symanzik Equation
20.6 Homogeneous Callan–Symanzik Equation
20.7 Renormalization Group for Non-Abelian Gauge Theories
20.8 Asymptotic Freedom
20.8.1 Electron–Positron Collision
20.8.2 Bjorken Scaling Law
20.9 Gauge Dependence of Green's Functions
21 Theory of Confinement
21.1 Gauge Independence of the Confinement Condition
21.2 Sufficient Condition for Colour Confinement
21.3 Colour Confinement and Asymptotic Freedom
22 Anomalous Terms and Dispersion Theory
22.1 Examples of Indefiniteness and Anomalous Terms
22.1.1 Vacuum Polarization
22.1.2 Goto–Imamura–Schwinger Term
22.1.3 Triangle Anomaly Term
22.1.4 Trace Anomaly Term
22.2 Dispersion Theory for Green's Functions
22.3 Subtractions in Dispersion Relations
22.4 Heisenberg Operators
22.5 Subtraction Condition
22.6 Anomalous Trace Identity
22.7 Triangle Anomaly Terms
22.7.1 Renormalization Condition
The Set {P }
The Set { W }
The Set { Aλ }
The Set { Cλ }
The Set { D }
The Set { B }
The Set { S }
22.7.2 Ward–Takahashi Identity for Cλ
22.7.3 Proof of the Adler–Bardeen Theorem Using the Callan–Symanzik Equation
Postface
References
Index