Functional Integrals in Quantum Field Theory and Statistical Physics

1. Functional Integrals and Quantum Mechanics.- 1. Introduction.- 2. Functional Integrals in Quantum Mechanics.- 3. Quantization of Systems with Constraints.- 4. Functional Integrals and Quantization on Manifolds.- 2. Functional Integrals in Quantum Field Theory and Statistical Physics.- 5. Functional Integrals and Perturbation Theory in Quantum Field Theory.- 6. Functional Integrals and the Temperature Diagram Technique in Statistical Physics.- 3. Gauge Fields.- 7. Quantization of Gauge Fields.- 8. Quantum Electrodynamics.- 9. Yang-Mills Fields.- 10. Quantization of a Gravitational Field.- 11. Attempts to Construct a Gauge-Invariant Theory of Electromagnetic and Weak Interactions.- 4. Infrared Asymptotics of Green’s Functions.- 12. Method of Successive Integration Over ‘Rapid’ and ‘Slow’ Fields.- 13. Infrared Asymptotic Behaviour of Green’s Functions in Quantum Electrodynamics.- 5. Scattering of High-Energy Particles.- 14. Double Logarithmic Asymptotics in Quantum Electro-dynamics.- 15. Eikonal Approximation.- 6. Superfluidity.- 16. Perturbation Theory for Superfluid Bose Systems.- 17. Bose Gas of Small Density.- 18. Application of Functional Integrals to the Derivation of Low-Energy Asymptotic Behaviour of the Green’s Function.- 19. Hydrodynamical Lagrangian of Nonideal Bose Gas.- 20. Superfluidity of Two-Dimensional and One-Dimensional Bose Systems.- 21. Quantum Vortices in a Bose Gas.- 7. Superconductivity.- 22. Perturbation Theory of Superconducting Fermi Systems.- 23. Superconductivity of the Second Kind.- 24. Bose Spectrum of Superfluid Fermi Gas.- 25. A System of the He3 Type.- 8. Plasma Theory.- 26. Hydrodynamical Action in Plasma Theory.- 27. Damping of Plasma Oscillations.- 9. The Ising Model.- 28. The Statistical Sum of the Ising Model as aFunctional Integral.- 29. The Correlation Function of the Ising Model.- 10. Phase Transitions.- 30. Special Role of Dimension d = 4.- 31. Calculation of Critical Indices and the Wilson Expansion.- 11. Vortex-Like Excitations in Relativistic Field Theory.- 32. Vortices in the Relativistic Goldstone Model.- 33. On Vortex-Like Solutions in Quantum Field Theory.- References.