Path Integrals, Hyperbolic Spaces, and Selberg Trace Formulae

By: Christian Grosche

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Hardcover | 1 December 1995

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Hardcover
292 Pages

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22.86 x 16.51 x 1.91

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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 discussion of integrable billiards in circles and spheres (flat and hyperbolic space) 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.

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Non-Fiction Mathematics Calculus & Mathematical Analysis Calculus Science Physics Quantum Physics & Quantum Mechanics & Quantum Field Theory Mathematical Physics Science in General Maths for Scientists Classical Mathematics Booktopia Publisher Services

World Scientific Publishing

List of Tables
List of Figures
Introduction	p. 1
Path Integrals in Quantum Mechanics	p. 8
Separable Coordinate Systems on Spaces of Constant Curvature	p. 34
Path Integrals in Pseudo-Euclidean Geometry	p. 50
Path Integrals in Euclidean Spaces	p. 75
Path Integrals on Spheres	p. 86
Path Integrals on Hyperboloids	p. 96
Additional Results on Path Integration in Hyperbolic Spaces	p. 120
Billiard Systems and Periodic Orbit Theory	p. 130
The Selberg Trace Formula	p. 147
The Selberg Super-Trace Formula	p. 188
Summary and Discussion	p. 224
Bibliography	p. 239
Index	p. 277
Table of Contents provided by Blackwell. All Rights Reserved.

Path Integrals, Hyperbolic Spaces, and Selberg Trace Formulae

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Hardcover

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