Path Integrals in Physics - Volume II

Volume II is devoted to quantum field theory and statistical physics. It deals with systems with an infinite number of degrees of freedom. The full mathematical foundation is not yet completely established in this case. However, the path integral approach has proved extremely useful for the understanding of the most complex problems in quantum field theory, cosmology, condensed matter physics, etc.

Each chapter is self-contained and can be considered as an independent textbook covering general physical background, concepts of the path integral approach used, followed by the most typical and important applications presented in detail as well as problems with either their solutions or hints how to solve them. Beginners can start with any of the first two chapters and switch to their field of interest. More experienced users can start straightforwardly with their preferred field, and eventually return to the early chapters if needed.

Contents

Preface to volume II.

3. Quantum Field Theory: the Path Integral Approach.

• Path integral formulation of the simplest quantum field theories.
• Path integral quantization of gauge field theories.
• Non-perturbative methods for the analysis of quantum field models in the path integral approach. Path integrals in the theory of gravitation, cosmology and string theory: advanced applications of path integrals.

• Basic concept of statistical physics.
• Field theory at non-zero temperature.
• Superfluidity, superconductivity, non-equilibrium statistical physics in the path integral formalism and stochastic quantization.
• Path integrals formalism and lattice systems.