𝔖 Bobbio Scriptorium
✦   LIBER   ✦

Path integrals, hyperbolic spaces, and Selberg trace formulae

✍ Scribed by C. Grosche

Book ID
127430870
Publisher
World Scientific
Year
1996
Tongue
English
Weight
2 MB
Category
Library
City
Singapore; River Edge, N.J
ISBN-13
9789810224318

No coin nor oath required. For personal study only.

✦ Synopsis

In this volume, a comprehensive review is given for path integration in two- and three-dimensional homogeneous spaces of constant curvature, including an enumeration of all 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. In addition, an overview is presented on some recent achievements in the theory of the Selberg trace formula on Riemann surfaces, its super generalization, and their use in mathematical physics and quantum chaos. The volume also contains results on the study of the properties of a particular integrable billiard system in the hyperbolic plane, a proposal concerning interbasis expansions for spheroidal coordinate systems in four-dimensional Euclidean space, and some further results derived from the Selberg (super-) trace formula.

πŸ“œ SIMILAR VOLUMES

Brownian Motion on the Hyperbolic Plane
Brownian Motion on the Hyperbolic Plane and Selberg Trace Formula
✍ Nobuyuki Ikeda; Hiroyuki Matsumoto πŸ“‚ Article πŸ“… 1999 πŸ› Elsevier Science 🌐 English βš– 301 KB

We will show that the relation of the heat kernels for the Schro dinger operators with uniform magnetic fields on the hyperbolic plane H 2 (the Maass Laplacians) and for the Schro dinger operators with Morse potentials on R is given by means of a one-dimensional Fourier transform in the framework of

Semiclassical Trace Formulas in Terms of
Semiclassical Trace Formulas in Terms of Phase Space Path Integrals
✍ Ayumu Sugita πŸ“‚ Article πŸ“… 2001 πŸ› Elsevier Science 🌐 English βš– 254 KB

Semiclassical trace formulas are examined using phase space path integrals. Our main concern in this paper is the Maslov index of the periodic orbit, which seems not fully understood in previous works. We show that the calculation of the Maslov index is reduced to a classification of connections on