Cover -- Half-title -- Series-title -- Title -- Copyright -- Dedication -- Contents -- Preface to the First Edition -- Preface to the Second Edition -- 0 Introduction -- 0.1 Gauge invariance -- 0.2 Reasons for gauge theories of strong and electroweak interactions -- QCD -- Electroweak theory -- 1 Classical fields, symmetries and their breaking -- 1.1 The action, equations of motion, symmetries and conservation laws -- Equations of motion -- Global symmetries -- Space-time transformations -- Examples -- 1.2 Classical field equations -- Scalar field theory and spontaneous breaking of global symmetries -- Spinor fields -- 1.3 Gauge field theories -- U(1) gauge symmetry -- Non-abelian gauge symmetry -- 1.4 From classical to quantum fields (canonical quantization) -- Scalar fields -- The Feynman propagator -- Spinor fields -- Symmetry transformations for quantum fields -- 1.5 Discrete symmetries -- Space reflection -- Time reversal -- Charge conjugation -- Summary and the CPT transformation -- CP violation in the neutral… -- Problems -- 2 Path integral formulation of quantum field theory -- 2.1 Path integrals in quantum mechanics -- Transition matrix elements as path integrals -- Matrix elements of position operators -- 2.2 Vacuum-to-vacuum transitions and the imaginary time formalism -- General discussion -- Harmonic oscillator -- Euclidean Green's functions -- 2.3 Path integral formulation of quantum field theory -- Green's functions as path integrals -- Action quadratic in fields -- Gaussian integration -- 2.4 Introduction to perturbation theory -- Perturbation theory and the generating functional -- Wick's theorem -- An example: four-point Green's function in LambdaPhi -- Momentum space -- 2.5 Path integrals for fermions -- Grassmann algebra -- Anticommuting c-numbers -- Dirac propagator.

2.6 Generating functionals for Green's functions and proper vertices -- effective potential -- Classification of Green's functions and generating functionals -- Effective action -- Spontaneous symmetry breaking and effective action -- Effective potential -- 2.7 Green's functions and the scattering operator -- Problems -- 3 Feynman rules for Yang-Mills theories -- 3.1 The Faddeev-Popov determinant -- Gauge invariance and the path integral -- Faddeev-Popov determinant -- Examples -- Non-covariant gauges -- 3.2 Feynman rules for QCD -- Calculation of the Faddeev-Popov determinant -- Feynman rules -- 3.3 Unitarity, ghosts, Becchi-Rouet-Stora transformation -- Unitarity and ghosts -- BRS and anti-BRS symmetry -- Problems -- 4 Introduction to the theory of renormalization -- 4.1 Physical sense of renormalization and its arbitrariness -- Bare and 'physical' quantities -- Counterterms and the renormalization conditions -- Arbitrariness of renormalization -- Final remarks -- 4.2 Classification of the divergent diagrams -- Structure of the UV divergences by momentum power counting -- Classification of divergent diagrams -- Necessary counterterms -- 4.3 LambdaPhi: low order renormalization -- Feynman rules including counterterms -- Calculation of Fig. 4.8(b) -- Comments on analytic continuation to… -- Lowest order renormalization -- 4.4 Effective field theories -- Problems -- 5 Quantum electrodynamics -- 5.1 Ward-Takahashi identities -- General derivation by the functional technique -- Examples -- 5.2 Lowest order QED radiative corrections by the dimensional regularization technique -- General introduction -- Vacuum polarization -- Electron self-energy correction -- Electron self-energy: IR singularities regularized by photon mass -- On-shell vertex correction -- 5.3 Massless QED -- 5.4 Dispersion calculation of O(Alpha) virtual corrections in massless QED….

Self-energy calculation -- Vertex calculation -- 5.5 Coulomb scattering and the IR problem -- Corrections of order Alpha -- IR problem to all orders in Alpha -- Problems -- 6 Renormalization group -- 6.1 Renormalization group equation (RGE) -- Derivation of the RGE -- Solving the RGE -- Green's functions for rescaled momenta -- RGE in QED -- 6.2 Calculation of the renormalization group functions Beta, Gamma, Gamma -- 6.3 Fixed points -- effective coupling constant -- Fixed points -- Effective coupling constant -- 6.4 Renormalization scheme and gauge dependence of the RGE parameters -- Renormalization scheme dependence -- Effective Alpha in QED -- Gauge dependence of the Beta-function -- Problems -- 7 Scale invariance and operator product expansion -- 7.1 Scale invariance -- Scale transformations -- Dilatation current -- Conformal transformations -- 7.2 Broken scale invariance -- General discussion -- Anomalous breaking of scale invariance -- 7.3 Dimensional transmutation -- 7.4 Operator product expansion (OPE) -- Short distance expansion -- Light-cone expansion -- 7.5 The relevance of the light-cone -- Electron-positron annihilation -- Deep inelastic hadron leptoproduction -- Wilson coefficients and moments of the structure function -- 7.6 Renormalization group and OPE -- Renormalization of local composite operators -- RGE for Wilson coefficients -- OPE beyond perturbation theory -- 7.7 OPE and effective field theories -- Problems -- 8 Quantum chromodynamics -- 8.1 General introduction -- Renormalization and BRS invariance -- counterterms -- Asymptotic freedom of QCD -- The Slavnov-Taylor identities -- 8.2 The background field method -- 8.3 The structure of the vacuum in non-abelian gauge theories -- Homotopy classes and topological vacua -- Physical vacuum -- Theta-vacuum and the functional integral formalism.

8.4 Perturbative QCD and hard collisions -- Parton picture -- Factorization theorem -- 8.5 Deep inelastic electron-nucleon scattering in first order QCD (Feynman gauge) -- Structure functions and Born approximation -- Deep inelastic quark structure functions in the first order in the strong coupling constant -- Final result for the quark structure functions -- Hadron structure functions -- probabilistic interpretation -- 8.6 Light-cone variables, light-like gauge -- 8.7 Beyond the one-loop approximation -- Comments on the IR problem in QCD -- Problems -- 9 Chiral symmetry -- spontaneous symmetry breaking -- 9.1 Chiral symmetry of the QCD lagrangian -- 9.2 Hypothesis of spontaneous chiral symmetry breaking in strong interactions -- 9.3 Phenomenological chirally symmetric model of the strong interactions (Sigma-model) -- 9.4 Goldstone bosons as eigenvectors of the mass matrix and poles of Green's functions in theories with elementary scalars -- Goldstone bosons as eigenvectors of the mass matrix -- General proof of Goldstone's theorem -- 9.5 Patterns of spontaneous symmetry breaking -- 9.6 Goldstone bosons in QCD -- 10 Spontaneous and explicit global symmetry breaking -- 10.1 Internal symmetries and Ward identities -- Preliminaries -- Ward identities from the path integral -- Comparison with the operator language -- Ward identities and short-distance singularities of the operator products -- Renormalization of currents -- 10.2 Quark masses and chiral perturbation theory -- Simple approach -- Approach based on use of the Ward identity -- 10.3 Dashen's theorems -- Formulation of Dashen's theorems -- Dashen's conditions and global symmetry broken by weak gauge interactions -- 10.4 Electromagnetic… -- Electromagnetic… -- Spectral function sum rules -- Results -- 11 Higgs mechanism in gauge theories -- 11.1 Higgs mechanism.

11.2 Spontaneous gauge symmetry breaking by radiative corrections -- 11.3 Dynamical breaking of gauge symmetries and vacuum alignment -- Dynamical breaking of gauge symmetry -- Examples -- Problems -- 12 Standard electroweak theory -- 12.1 The lagrangian -- 12.2 Electroweak currents and physical gauge boson fields -- 12.3 Fermion masses and mixing -- 12.4 Phenomenology of the tree level lagrangian -- Effective four-fermion interactions -- Z couplings -- 12.5 Beyond tree level -- Renormalization and counterterms -- Corrections to gauge boson propagators -- Fermion self-energies -- Running Alpha(µ) in the electroweak theory -- Muon decay in the one-loop approximation -- Corrections to the Z partial decay widths -- 12.6 Effective low energy theory for electroweak processes -- QED as the effective low energy theory -- 12.7 Flavour changing neutral-current processes -- QCD corrections to CP violation in the neutral kaon system -- Problems -- 13 Chiral anomalies -- 13.1 Triangle diagram and different renormalization conditions -- Introduction -- Calculation of the triangle amplitude -- Different renormalization constraints for the triangle amplitude -- Important comments -- 13.2 Some physical consequences of the chiral anomalies -- Chiral invariance in spinor electrodynamics -- Pi… -- Chiral anomaly for the axial U(1) current in QCD… -- Anomaly cancellation in the SU(2) × U(1) electroweak theory -- Anomaly-free models -- 13.3 Anomalies and the path integral -- Introduction -- Abelian anomaly -- Non-abelian anomaly and gauge invariance -- Consistent and covariant anomaly -- 13.4 Anomalies from the path integral in Euclidean space -- Introduction -- Abelian anomaly with Dirac fermions -- Non-abelian anomaly and chiral fermions -- Problems -- 14 Effective lagrangians -- 14.1 Non-linear realization of the symmetry group -- Non-linear Sigma-model.

Effective lagrangian in the….