Quantum field theory : by Academician Prof. Kazuhiko Nishijima - a classic in theoretical physics / Kazuhiko Nishijima ; Masud Chaichian, Anca Tureanu, editors.

Format:

Book

Author/Creator:

Nishijima, K. (Kazuhiko), 1926-2009, author.

Contributor:

Chaichian, Masud, editor.

Tureanu, Anca, editor.

Series:

Physics and Astronomy Series

Language:

English

Subjects (All):

Quantum field theory.

Physical Description:

1 online resource (571 pages)

Edition:

1st ed.

Place of Publication:

Dordrecht, The Netherlands : Springer, [2023]

Summary:

This book is a translation of the 8th edition of Prof.Kazuhiko Nishijima's classical textbook on quantum field theory.It is based on the lectures the Author gave to students and researchers with diverse interests over several years in Japan.

Contents:

Intro

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.

Notes:

Includes bibliographical references and index.

Description based on print version record.

Description based on publisher supplied metadata and other sources.

Other Format:

Print version: Nishijima, Kazuhiko Quantum Field Theory

ISBN:

94-024-2190-4

OCLC:

1351198992