PATH INTEGRALS, HYPERBOLIC SPACES AND SELBERG TRACE FORMULAE (2ND EDITION) - Hardcover

GROSCHE CHRISTIAN

 
9789814460071: PATH INTEGRALS, HYPERBOLIC SPACES AND SELBERG TRACE FORMULAE (2ND EDITION)
Hardcover
ISBN 10: 9814460079 ISBN 13: 9789814460071
Publisher: World Scientific, 2013

Synopsis

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.

"synopsis" may belong to another edition of this title.

From the Back Cover

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.

"About this title" may belong to another edition of this title.

Publisher
World Scientific
Publication date
2013
Language
English
ISBN 10 
9814460079
ISBN 13 
9789814460071
Binding
Hardcover
Edition number
2
Number of pages
388