Path Integrals in Physics

By M. Chaichian, A. Demichev. 2018

197 citations recorded by the source corpus.

Volume 1: 1 Path Integrals in Classical Theory. Brownian motion: Introduction to the concept of parth integration. Wiener path integrals and stochastic processes. 2 Path integrals in Quantum Mechanics. Feynman path integrals. Path integrals inHamiltonian formalism. Quantizations, the operator ordering problem and path integrals. Path integrals and quantizations in spaces with topologiecal constraints. Path integrals in curved spaces, space time transformations and the Coulomb problem. Pathintegrals over anticommuting variables for fermions and generalisations. Appendices. Bibliography. Index.Volume 2: 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 thepath integral approach. Path integrals in the theory of gravitation, cosmology and string theory: advanced applications of path integrals. 4. Path Integrals in Statistical Physics. Basic concept of statistical physics. Field theory at non-zerotemperature. Superfluidity, superconductivity, non-equilibrium statistical physics in the path integral formalism and stochastic quantization. Path integrals formalism and lattice systems. Supplements. Bibliography. Index

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Citations in the corpus

Path Integrals and Anomalies in Curved Space: Nonlinear susy sigma models and d = 1 superspace (2006, background): “The formalism for path integrals in curved space has been discussed in great generality in several books and reviews [7, 8, 9, 10, 11, 12, 13, 14, 15].”
Stochastic thermodynamics, fluctuation theorems and molecular machines (2012, background): “More technical background concerning these three equivalent descriptions of Markovian stochastics dynamics of a continuous degree of freedom is provided in the monographs [50, 51, 52, 53].”
UNIVERSAL SCALING BEHAVIOR OF NON-EQUILIBRIUM PHASE TRANSITIONS (2004, unknown): “[171]).”
Unified cosmic history in modified gravity: From F ( R ) theory to Lorentz non-invariant models (2010, background): “Of course, the classical and quantum dynamics of such constrained theories are quite non-trivial [117].”