Quantum Field Theory

ISBN-13: 9789402421927 / Angielski / Miękka / 2024

Kazuhiko Nishijima

Opis

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. The book includes both the historical development of QFT and its practical use in theoretical and experimental particle physics, presented in a pedagogical and transparent way and, in several parts, in a unique and original manner. The Author, Academician Nishijima, is the inventor (independently from Murray Gell-Mann) of the third (besides the electric charge and isospin) quantum number in particle physics: strangeness. He is also most known for his works on several other theories describing particles such as electron and muon neutrinos, and his work on the so-called Gell-Mann–Nishijima formula.The present English translation from its 8^th Japanese edition has been initiated and taken care of by the editors Prof. M. Chaichian and Dr. A. Tureanu from the University of Helsinki, who were close collaborators of Prof. Nishijima. Dr. Yuki Sato, a researcher in particle physics at the University of Nagoya, most kindly accepted to undertake the heavy task of translation. The translation of the book can be regarded as a tribute to Prof. Nishijima's memory, for his fundamental contributions to particle physics and quantum field theory.The book presents with utmost clarity and originality the most important topics and applications of QFT which by now constitute the established core of the theory. It is intended for a wide circle of graduate and post-graduate students, as well as researchers in theoretical and particle physics. In addition, the book can be a useful source as a basic material or supplementary literature for lecturers giving a course on quantum field theory.

Spis treści

1 Elementary Particle Theory and Field Theory

1.1 Classification of Interactions and Yukawa’s Theory

1.2 Muon as the First Member of the Second Generation

1.3 Quantum Electrodynamics

1.4 Road from Pions to Hadrons

1.5 Strange Particles as Members of the Second Generation

1.6 Non-conservation of Parity

1.7 Neutrino in the Second Generation

1.8 Democracy and Aristocratism of Hadrons—Quark Model

2 Canonical Formalism and Quantum Mechanics

2.1 Schr¨odinger’s Picture and Heisenberg’s Picture

2.2 Hamilton’s Principle

2.3 Equivalence between Canonical Equation and Lagrange’s Equation

2.4 Equal-Time Canonical Commutation Relations

3 Quantisation of Free Fields

3.1 Field Theory Based on Canonical Formalism

3.2 Relativistic Generalisation of Canonical Equation

3.3 Quantisation of Real Scalar Field

3.4 Quantisation of Complex Scalar Field

3.5 Dirac’s Equation

3.6 Relativistic Invertibilities of Dirac’s Wave Function

3.7 Solutions of Free Dirac’s Equation

3.8 Quantisation of the Dirac Field

3.9 Charge Conjugation

3.10 Quantisation of Complex Vector Field

4 Invariant Functions and Quantisation of Free Fields

4.1 Unequal-time Commutation Relations of Real Scalar Field

4.2 Various Sorts of Invariant Functions

4.3 Unequal-time Commutation Relations of Free Fields

4.4 Generality of Quantisation of Free Fields

5 Indefinite Metric and Electromagnetic Field

5.1 Indefinite Metric

5.2 Generalised Eigenstates

5.3 Free Electromagnetic Field—Fermi’s Gauge

5.4 Lorentz Condition and Physical State Space

5.5 Free Electromagnetic Field—Generalisation of Gauge Choices

6 Quantisation of Interacting Systems

6.1 Tomonaga-Schwinger Equation

6.2 Retarded Product Expansion of Heisenberg’s Operators

6.3 Yang-Feldman Expansion of Heisenberg’s 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 Examples of Noether’s Theorem

7.4 Poincar´e Invariance

7.5 Representations of Lorentz Group

7.6 Spin of a Massless Particle

7.7 Pauli-G¨ursey Group

8 S-Matrix

8.1 Definition of S-Matrix

8.2 Dyson’s Formula for S-Matrix

8.3 Wick’s Theorem

8.4 Feynman Diagrams

8.5 Examples of S-Matrix Elements

8.6 Furry’s Theorem

8.7 Two-Photon Decays of Neutral Mesons

9 Cross Sections and Decay Widths

9.1 Møller’s Formula for Cross Sections and Formula of

Decay Widths

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 Anti-unitary 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 Time-Orderings in Lagrangian Formalism

11.4 Matthews’ Theorem

11.5An Example of Matthews’ Theorem with Modification

11.6 Reduction Formula in the Interaction Picture

11.7 Asymptotic Conditions

11.8 Unitarity Condition on Green’s Function

11.9 Retarded Green’s Functions

12 Renormalisation Theory

12.1 Lippmann-Schwinger Equation

12.2 Renormalised Interaction Picture

12.3 Renormalisation of Masses

12.4 Renormalisation of Field Operators

12.5 Renormalised Propagators

12.6 Renormalisation of Vertex Functions

12.7 Ward-Takahashi Identity

12.8 Integral Representation of Propagator

13 Classification of Hadrons and Models

13.1 Unitary Groups

13.2 SU(3) Group

13.3 Universality of p-Meson Decay Interactions

13.4 Beta-Decay

13.5 Universality of Fermi’s Interaction

13.6 Quark Model in Weak Interactions

13.7 Quark Model in Strong Interactions

13.8 Parton Model

14 What is Gauge Theory?

14.1Gauge Transformation of Electromagnetic Field

14.2 Non-Abelian Gauge Field

14.3 Gravitational Field as Gauge Field

15 Spontaneous Symmetry Breaking

15.1 Nambu-Goldstone Particles

15.2 Sigma Model

15.3 Mechanism of Spontaneous Symmetry Breaking

15.4 Higgs Mechanism

15.5 Higgs Mechanism under Covariant Gauge Condition

15.6 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 Method

17.1 Quantisation of a Point-Particle System

17.2 Quantisation of Fields

18 Quantisation of Gauge Fields via Path Integral Method

18.1 Quantisation of Gauge Fields

18.2 Quantisation of Electromagnetic

18.3 Quantisation of Non-Abelian Gauge Fields

18.4 Axial Gauge

18.5 Feynman Rule in Axial 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 BRS Algebra

19.6 Unitarity of S-Matrix

19.7 Representations of Extended BRS Algebra

19.8 Representations of BRS Transformations for Auxiliary Fields

19.9 Representations of BRSNO Algebras

20 Renormalisation Group

20.1 Renormalisation Group for QED

20.2 Approximate Equations for Renormalisation Group

20.3 Ovsianikov’s Equation

20.4 Linear Equations for Renormalisation Group

20.5 Callan-Symanzik Equation

20.6Homogeneous Callan-Symanzik Equation

20.7 Renormalisation Group for Non-Abelian Gauge Theory

20.8 Asymptotic Freedom

20.9Gauge Dependence of Green’s Functions

21 Theory of Confinement

21.1Gauge Independence of Confinement Condition

21.2 Sufficient Condition for Colour Confinement

21.3 Colour Confinement and Asymptotic Freedom

22 Anomalous Terms and Dispersion

22.1 Examples of Indefiniteness and Anomalous

22.2 Dispersion Theory for Green’s

22.3 Subtractions in Dispersion Relation

22.4 Heisenberg’s

22.5 Subtraction

22.6 Anomalous Trace

22.7 Triangle-Anomaly Terms

O autorze

Kazuhiko Nishijima (1926 – 2009) was a Japanese physicist who made significant contributions to particle physics. Until his death in 2009 he was Professor Emeritus at the University of Tokyo and Kyoto University. He is most well-known for his work on the Gell-Mann–Nishijima formula, and the concept of strangeness. He was nominated for the Nobel Prize in Physics in 1960 and 1961.

Prof. Masud Chaichian and Dr. Anca Tureanu are physicists at University of Helsinki. They were close collaborators of Prof. Nishijima.

Yuki Sato is Associate Professor at National Institute of Technology, Tokuyama College and visiting faculty member at Nagoya University.