Path integrals, hyperbolic spaces, and Selberg trace formulae
著者
書誌事項
Path integrals, hyperbolic spaces, and Selberg trace formulae
World Scientific, c1996
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注記
Includes bibliographical references (p. 239-276)
内容説明・目次
内容説明
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.
目次
- Path integrals in quantum mechanics
- separable co-ordinate systems
- path integrals in pseudo-Euclidean geometry
- path integrals in Euclidean spaces
- path integrals on spheres
- path integrals on hyperboloids
- path integration in hyperbolic spaces
- billiard systems and periodic orbit theory
- the Selberg trace formula
- the Selberg super trace formula
- summary and discussion.
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