Preface 1. Gaussian integrals. Algebraic preliminaries 2. Euclidean path integrals and quantum mechanics 3. Quantum mechanics: Path integrals in phase space 4. Quantum statistical physics: Functional integration formalism 5. Quantum evolution: From particles to fields 6. The neutral relativistic scalar field 7.
Perturbative quantum field theory: Algebraic methods 8. Ultraviolet divergences: Effective quantum field theory 9. Introduction to renormalization theory and renormalization group 10. Dimensional continuation, regularization. Minimal subtraction, RG functions 11. Renormalization of local polynomials. Short distance expansion 12. Relativistic fermions: Introduction 13.
Symmetries, chiral symmetry breaking and renormalization 14. Critical phenomena: General considerations. Mean-field theory 15. The renormalization group approach: The critical theory near dimension 4 16. Critical domain: Universality, "-expansion 17. Critical phenomena: Corrections to scaling behaviour 18. O(N)-symmetric vector models for N large 19. The non-linear ?-model near two dimensions: Phase structure 20.
Gross-Neveu-Yukawa and Gross-Neveu models 21. Abelian gauge theories: The framework of quantum electrodynamics 22. Non-Abelian gauge theories: Introduction 23. The Standard Model of fundamental interactions 24. Large momentum behaviour in quantum field theory 25. Lattice gauge theories: Introduction 26. BRST symmetry, gauge theories: Zinn-Justin equation and renormalization 27. Supersymmetric quantum field theory: Introduction 28.
Elements of classical and quantum gravity 29. Generalized non-linear ?-models in two dimensions 30. A few two-dimensional solvable quantum field theories 31. O(2) spin model and Kosterlitz-Thouless's phase transition 32. Finite-size effects in field theory. Scaling behaviour 33. Quantum field theory at finite temperature: Equilibrium properties 34. Stochastic differential equations: Langevin, Fokker-Planck equations 35.
Langevin field equations, properties and renormalization 36. Critical dynamics and renormalization group 37. Instantons in quantum mechanics 38. Metastable vacua in quantum field theory 39. Degenerate classical minima and instantons 40. Perturbative expansion at large orders 41. Critical exponents and equation of state from series summation 42. Multi-instantons in quantum mechanics Bibliography Index.