Path Integrals, Hyperbolic Spaces And Selberg Trace Formulae (2nd Edition‪)‬

In this second edition, a comprehensive review is given for path integration in two- and three-dimensional (homogeneous) spaces of constant and non-constant curvature, including an enumeration of all the corresponding coordinate systems which allow separation of variables in the Hamiltonian and in the path integral. The corresponding path integral solutions are presented as a tabulation. Proposals concerning interbasis expansions for spheroidal coordinate systems are also given. In particular, the cases of non-constant curvature Darboux spaces are new in this edition.

The volume also contains results on the numerical study of the properties of several integrable billiard systems in compact domains (i.e. rectangles, parallelepipeds, circles and spheres) in two- and three-dimensional flat and hyperbolic spaces. In particular, the discussions of integrable billiards in circles and spheres (flat and hyperbolic spaces) and in three dimensions are new in comparison to the first edition.

In addition, an overview is presented on some recent achievements in the theory of the Selberg trace formula on Riemann surfaces, its super generalization, their use in mathematical physics and string theory, and some further results derived from the Selberg (super-) trace formula.Contents:

Introduction
Path Integrals in Quantum Mechanics
Separable Coordinate Systems on Spaces of Constant Curvature
Path Integrals in Pseudo-Euclidean Geometry
Path Integrals in Euclidean Spaces
Path Integrals on Spheres
Path Integrals on Hyperboloids
Path Integral on the Complex Sphere
Path Integrals on Hermitian Hyperbolic Space
Path Integrals on Darboux Spaces
Path Integrals on Single-Sheeted Hyperboloids
Miscellaneous Results on Path Integration
Billiard Systems and Periodic Orbit Theory
The Selberg Trace Formula
The Selberg Super-Trace Formula
Summary and Discussion


Graduate and researchers in mathematical physics. Key Features:


The 2nd edition brings the text up to date with new developments and results in the field
Contains enumeration of many explicit path integrals solutions