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

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 Schrodinger’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 Poincare Invariance 7.5 Representations of Lorentz Group 7.6 Spin of a Massless Particle 7.7 Pauli-Gursey 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 Mller’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