Preface -- 1 Basics of elementary particles -- 1.1 Fundamental particles -- 1.1.1 Fermions -- 1.1.2 Vector bosons -- 1.2 Fundamental interactions -- 1.3 The Standard Model and perspectives -- 2 Lagrange formalism. Symmetries and gauge fields -- 2.1 Lagrange mechanics of a particle -- 2.2 Real scalar field. Lagrange equations -- 2.3 The Noether theorem -- 2.4 Complex scalar and electromagnetic fields -- 2.5 Yang-Mills fields -- 2.6 The geometry of gauge fields -- 2.7 A realistic example - chromodynamics -- 3 Canonical quantization, symmetries in quantum field theory -- 3.1 Photons -- 3.1.1 Quantization of the electromagnetic field -- 3.1.2 Remarks on gauge invariance and Bose statistics -- 3.1.3 Vacuum fluctuations and Casimir effect -- 3.2 Bosons -- 3.2.1 Scalar particles -- 3.2.2 Truly neutral particles -- 3.2.3 CPT-transformations -- 3.2.4 Vector bosons -- 3.3 Fermions -- 3.3.1 Three-dimensional spinors -- 3.3.2 Spinors of the Lorentz group -- 3.3.3 The Dirac equation -- 3.3.4 The algebra of Dirac's matrices -- 3.3.5 Plane waves -- 3.3.6 Spin and statistics -- 3.3.7 C, P, T transformations for fermions -- 3.3.8 Bilinear forms -- 3.3.9 The neutrino -- 4 The Feynman theory of positron and elementary quantum electrodynamics -- 4.1 Nonrelativistic theory. Green's functions -- 4.2 Relativistic theory -- 4.3 Momentum representation -- 4.4 The electron in an external electromagnetic field -- 4.5 The two-particle problem -- 5 Scattering matrix -- 5.1 Scattering amplitude -- 5.2 Kinematic invariants -- 5.3 Unitarity -- 6 Invariant perturbation theory -- 6.1 Schroedinger and Heisenberg representations -- 6.2 Interaction representation -- 6.3 S-matrix expansion -- 6.4 Feynman diagrams for electron scattering in quantum electrodynamics -- 6.5 Feynman diagrams for photon scattering -- 6.6 Electron propagator.

6.7 The photon propagator -- 6.8 The Wick theorem and general diagram rules -- 7 Exact propagators and vertices -- 7.1 Field operators in the Heisenberg representation and interaction representation -- 7.2 The exact propagator of photons -- 7.3 The exact propagator of electrons -- 7.4 Vertex parts -- 7.5 Dyson equations -- 7.6 Ward identity -- 8 Some applications of quantum electrodynamics -- 8.1 Electron scattering by static charge: higher order corrections -- 8.2 The Lamb shift and the anomalous magnetic moment -- 8.3 Renormalization - how it works -- 8.4 "Running" the coupling constant -- 8.5 Annihilation of e+e~ into hadrons. Proof of the existence of quarks -- 8.6 The physical conditions for renormalization -- 8.7 The classification and elimination of divergences -- 8.8 The asymptotic behavior of a photon propagator at large momenta . -- 8.9 Relation between the "bare" and "true" charges -- 8.10 The renormalization group in QED -- 8.11 The asymptotic nature of a perturbation series -- 9 Path integrals and quantum mechanics -- 9.1 Quantum mechanics and path integrals -- 9.2 Perturbation theory -- 9.3 Functional derivatives -- 9.4 Some properties of functional integrals -- 10 Functional integrals: scalars and spinors -- 10.1 Generating the functional for scalar fields -- 10.2 Functional integration -- 10.3 Free particle Green's functions -- 10.4 Generating the functional for interacting fields -- 10.5 f4 theory -- 10.6 The generating functional for connected diagrams -- 10.7 Self-energy and vertex functions -- 10.8 The theory of critical phenomena -- 10.9 Functional methods for fermions -- 10.10 Propagators and gauge conditions in QED -- 11 Functional integrals: gauge fields -- 11.1 Non-Abelian gauge fields and Faddeev-Popov quantization -- 11.2 Feynman diagrams for non-Abelian theory.

12 The Weinberg-Salam model -- 12.1 Spontaneous symmetry-breaking and the Goldstone theorem -- 12.2 Gauge fields and the Higgs phenomenon -- 12.3 Yang-Mills fields and spontaneous symmetry-breaking -- 12.4 The Weinberg-Salam model -- 13 Renormalization -- 13.1 Divergences in f4 -- 13.2 Dimensional regularization of f4-theory -- 13.3 Renormalization of f4-theory -- 13.4 The renormalization group -- 13.5 Asymptotic freedom of the Yang-Mills theory -- 13.6 "Running" coupling constants and the "grand unification" -- 14 Nonperturbative approaches -- 14.1 The lattice field theory -- 14.2 Effective potential and loop expansion -- 14.3 Instantons in quantum mechanics -- 14.4 Instantons and the unstable vacuum in field theory -- 14.5 The Lipatov asymptotics of a perturbation series -- 14.6 The end of the "zero-charge" story? -- Bibliography -- Index.