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Path Integrals, Hyperbolic Spaces And Selberg Trace Formulae

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Title: Path Integrals, Hyperbolic Spaces And Selberg Trace Formulae
Description: 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.
Authors: Christian Grosche
Resource Type: eBook.
Subjects: Path integrals, Quantum theory
Categories: SCIENCE / Physics / Mathematical & Computational, MATHEMATICS / Geometry / Non-Euclidean, SCIENCE / Physics / Quantum Theory
Database: eBook Collection (EBSCOhost)
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Header DbId: nlebk
DbLabel: eBook Collection (EBSCOhost)
An: 637088
RelevancyScore: 1051
AccessLevel: 6
PubType: eBook
PubTypeId: ebook
PreciseRelevancyScore: 1050.81640625
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  Data: 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.
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  Data: <searchLink fieldCode="DE" term="%22Path+integrals%22">Path integrals</searchLink><br /><searchLink fieldCode="DE" term="%22Quantum+theory%22">Quantum theory</searchLink>
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  BibEntity:
    Classifications:
      – Code: 530.12
        Scheme: ddc
        Type: prePub
    Languages:
      – Code: eng
        Text: English
    Subjects:
      – SubjectFull: Path integrals
        Type: general
      – SubjectFull: Quantum theory
        Type: general
    Titles:
      – TitleFull: Path Integrals, Hyperbolic Spaces And Selberg Trace Formulae
        Type: main
  BibRelationships:
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      – PersonEntity:
          Name:
            NameFull: Christian Grosche
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            NameFull: Christian Grosche
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          Dates:
            – D: 01
              M: 01
              Type: published
              Y: 2013
            – D: 04
              M: 02
              Type: profile
              Y: 2014
          Identifiers:
            – Type: isbn-print
              Value: 9789814460071
            – Type: isbn-electronic
              Value: 9789814460088
            – Type: isbn-electronic
              Value: 9789814460095
          Titles:
            – TitleFull: Path Integrals, Hyperbolic Spaces And Selberg Trace Formulae
              Type: main
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