Quantum Field Theory

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Quantum Field Theory, Second Edition Abstract Half-Title Title-Page Copyright Dedication Contents Preface to the first edition Preface to the second edition 1 Introduction: synopsis of particle physics 1.1 Quantum field theory 1.2 Gravitation 1.3 Strong interactions 1.4 Weak interactions 1.5 Leptonic quantum numbers 1.6 Hadronic quantum numbers 1.7 Resonances 1.8 The quark model 1.9 SU(2), SU(3), SU(4), … 1.10 Dynamical evidence for quarks 1.11 Colour 1.12 QCD 1.13 Weak interactions Guide to further reading 2 Single-particle relativistic wave equations 2.1 Relativistic notation 2.2 Klein–Gordon equation 2.3 Dirac equation SU(2) and the rotation group SL(2, C) and the Lorentz group 2.4 Prediction of antiparticles 2.5 Construction of Dirac spinors: algebra of [gamma] matrices 2.6 Non-relativistic limit and the electron magnetic moment 2.7 The relevance of the Poincaré group: spin operators and the zero mass limit 2.8 Maxwell and Proca equations 2.9 Maxwell's equations and differential geometry Summary Guide to further reading 3 Lagrangian formulation, symmetries and gauge fields 3.1 Lagrangian formulation of particle mechanics 3.2 The real scalar field: variational principle and Noether's theorem 3.3 Complex scalar fields and the electromagnetic field 3.4 Topology and the vacuum: the Bohm–Aharonov effect 3.5 The Yang–Mills field 3.6 The geometry of gauge fields Summary Guide to further reading 4 Canonical quantisation and particle interpretation 4.1 The real Klein–Gordon field 4.2 The complex Klein–Gordon field 4.3 The Dirac field 4.4 The electromagnetic field Radiation gauge quantisation Lorentz gauge quantisation 4.5 The massive vector field Summary Guide to further reading 5 Path integrals and quantum mechanics 5.1 Path-integral formulation of quantum mechanics 5.2 Perturbation theory and the S matrix 5.3 Coulomb scattering 5.4 Functional calculus: differentiation 5.5 Further properties of path integrals Appendix: some useful integrals Summary Guide to further reading 6 Path-integral quantisation and Feynman rules: scalar and spinor fields 6.1 Generating functional for scalar fields 6.2 Functional integration 6.3 Free particle Green's functions 6.4 Generating functionals for interacting fields 6.5 phi-4 theory Generating functional 2-point function 4-point function 6.6 Generating functional for connected diagrams 6.7 Fermions and functional methods 6.8 The S matrix and reduction formula 6.9 Pion–nucleon scattering amplitude 6.10 Scattering cross section Summary Guide to further reading 7 Path-integral quantisation: gauge fields 7.1 Propagators and gauge conditions in QED Photon propagator – canonical formalism Photon propagator – path-integral method Gauge-fixing terms Propagator for transverse photons 7.2 Non-Abelian gauge fields and the Faddeev–Popov method Feynman rules in the Lorentz gauge Gauge-field propagator in the axial gauge 7.3 Self-energy operator and vertex function Geometrical interpretation of the Legendre transformation Thermodynamic analogy 7.4 Ward–Takahashi identities in QED 7.5 Becchi–Rouet–Stora transformation 7.6 Slavnov–Taylor identities 7.7 A note on ghosts and unitarity Summary Guide to further reading 8 Spontaneous symmetry breaking and the Weinberg–Salam model 8.1 What is the vacuum? 8.2 The Goldstone theorem 8.3 Spontaneous breaking of gauge symmetries 8.4 Superconductivity 8.5 The Weinberg–Salam model Summary Guide to further reading 9 Renormalisation 9.1 Divergences in phi-4 theory Dimensional analysis 9.2 Dimensional regularisation of phi-4 theory Loop expansion 9.3 Renormalisation of phi-4 theory Counter-terms 9.4 Renormalisation group 9.5 Divergences and dimensional regularisation of QED 9.6 1-loop renormalisation of QED Anomalous magnetic moment ofthe electron Asymptotic behaviour 9.7 Renormalisability of QED 9.8 Asymptotic freedom of Yang–Mills theories 9.9 Renormalisation of pure Yang–Mills theories 9.10 Chiral anomalies Cancellation of anomalies 9.11 Renormalisation of Yang–Mills theories with spontaneous symmetry breakdown 't Hooft's gauges The effective potential Loop expansion of the effective potential Appendix A: integration in d dimensions Appendix B: the gamma function Summary Guide to further reading 10 Topological objects in field theory 10.1 The sine–Gordon kink 10.2 Vortex lines 10.3 The Dirac monopole 10.4 The 't Hooft–Polyakov monopole 10.5 Instantons Quantum tunnelling, [theta]-vacua and symmetry breaking Summary Guide to further reading 11 Supersymmetry 11.1 Introduction 11.2 Lorentz transformations; Dirac, Weyl and Majorana spinors Some further relations 11.3. Simple Lagrangian model Digression: Fierz rearrangement formula 11.4 Simple Lagrangian model (cont.): closure of commutation relations Mass term 11.5 Towards a super-Poincaré algebra 11.6 Superspace 11.7 Superfields Chiral superfield 11.8 Recovery of the Wess–Zumino model Appendix: some 2-spinor conventions Summary Guide to further reading References Index A B C D E F G H I J K L M N O P Q R S T U V W Y Z Back Cover