1 Introduction 1.1 Preface and conventions 1.2 Why quantum field theory? 2 quantum theory of free scalar fields 2.1 Local fields 2.2 Problems for Chapter 2 3 Interacting field theory 3.1 Schwinger-Dyson equations and functional integrals 3.2 Functional integral solution of he SD equations 3.3 Perturbation theory 3.4 Connected and 1-P(article) I(rreducible) Green functions 3.5 Legendres trees 3.6 The ICdillen Lehmann spectral representation 3.7 The scattering matrix and the LSZ formula 3.8 Problems for Chapter 3 4 Particles of spin 1, and gauge invariance 4.1 Massive spinning particles 4.2 Massless particles with helicity 4.3 Field theory for massive spin-1 particles 4.4 Problems for Chapter 4 5 Spin-particles and Fermi statistics 5.1 Dirac, Majorana, and Weyl fields: discrete symmetries 5.2 The functional formalism for fermion fields 5.3 Feynman rules for Dirac fermions 5.4 Problems for Chapter 5 6 Massive quantum electrodynamics 6.1 Free the longitudinal gauge bosons! 6.2 Heavy-fermion production in electron-positron annihilation 6.3 Interaction with heavy fermions: particle paths and external fields 6.4 The magnetic moment of a weakly coupled charged particle 6.5 Problems for Chapter 6 7 Symmetries, Ward identities, and Nambu-Goldstone bosons 7.1 Space-time symmetries 7.2 Spontaneously broken symmetries 7.3 Nambu-Goldstone bosons in the semi-classical expansion 7.4 Low-energy effective field theory of Nambu Goldstone bosons 7.5 Problems for Chapter 7 8 Non-abelian gauge theory 8.l The non-abelian Higgs phenomenon 8.2 BRST symmetry 8.3 A brief history of the physics of non-abelian gauge theory 8.4 The Higgs model, aty, and the phases of gauge theory 8.5 Confinement ofmonopoles in the Higgs phase 8.6 The electro-weak sector of the standard model 8.7 Symmetries and symmetry breaking in the strong interactions 8.8 Anomalies 8.9 ntization of gauge theories in the Higgs phase 8.10 Problems for Chapter 8 9 Renormalizati0n and effective field theory 9.1 Divergences in Feynman graphs 9.2 Cut-offs 9.3 Renormalization and critical phenomena 9.4 The renormalization (semi-)group in field theory 9.5 Mathematical (Lorentz-invariant, unitary) quantum field theory 9.6 Renormalization of 4 field theory 9.7 Renormalization-group equations in dimensional regularization 9.8 Renormalization of ED at one loop 9.9 Renormalization-group equations in ED 9.10 Whyis ED IR-free? 9.11 Coupling renormalization in non-abelian gauge theory 9.12 Renormalization-group equatinns for masses and the hierarchy problem 9.13 Renormalization-group equations for the S-matrix 9.14 Renormalization and symmetry 9.15 The standard model throu&nsp;the lens of renormalizatinn 9.16 Problems for Chapter 9 10 Instantons and solitons 100.1 The most probable escape path 10.2 Instantons in quantum mechanics 10.3 Instantons and solitons in field theory 10.4 Instantons in the two-dimensional Higgs model 10.5 Monopole instantons in three-dimensional Higgs models 10.6 Yan Mills instantons 10.7 Solitons 10.8 Hooft Polyakov monopoles 10.9 Problems for Chapter 10 11 Concluding remarks Appendix A Books Appendix B Cross sections Appendix C Diracology Appendix D Feynman rules Appendix E Group theory and Lie algebras Appendix F Everything else References Author index Subiect index