Path Integrals in Physics

This book expounds the fundamentals of path integrals, of both the Wiener and Feynman type, and their many applications in physics. It is based on many courses given by the authors for students and researchers in physics and mathematics. It provides a comprehensive, detailed and systematic account of the subject suitable for both students and experienced researchers.

Contents

1. Path Integrals in Classical Theory.

• Brownian Motion: Introduction to the concept of path integration.
• Wiener path integrals and Stochastic Processes.

• Feynman Path Integrals.
• Path Integrals in Hamiltonian Formalism.
• Quantization, the Operator Ordering Problem and Path Integrals.
• Path Integrals and Quantizations in Spaces with Topological Constraints.
• Path Integrals in Curved Spaces, Space-time Transformations and the Coulomb Problem.
• Path Integrals over Anticommuting Variables for Fermions and Generalizations.

• Appendices.
• Bibliography.
• Index.

This book expounds the fundamentals of path integrals, of both the Wiener and Feynman type, and their many applications in physics. It is based on many courses given by the authors for students and researchers in physics and mathematics. It provides a comprehensive, detailed and systematic account of the subject suitable for both students and experienced researchers.

Contents

3. Quantum Field Theory: The Path Integral Approach.

• Path Integral Formation of the Simplest Quantum Field Theories.
• Non-perturbable 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.
• Supplements.
• Bibliography.
• Index.