Description
Book SynopsisThis 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 8th 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.
Table of Contents1 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
