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Path integrals over manifolds

  • V. Quantization Methods
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Differential Geometric Methods in Mathematical Physics

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 905))

Abstract

Path integrals are considered for the cases where the underlying manifold is multiply connected or non-flat. In case of multiple connectivity, the contributions of different homotopy classes of paths are analyzed with the help of covering spaces. In case of a non-flat manifold, it is pointed out that a judicious choice of the free Hamiltonian operator and of normalizing factors can eliminate the explicit occurrence of the scalar curvature. (A heuristic approach to path integrals is adopted in case of non-flat spaces.)

The present article constitutes a revised text of a seminar which the author gave at a summer school at T.U. Clausthal in 1979. This article is included in the present proceedings by a special arrangement with the editors.

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Author information

Authors and Affiliations

  1. Institut für Theoretische Physik, T.U. Clausthal, 3392, Clausthal-Zellerfeld, Fed. Rep. of Germany

    Jan Tarski

Authors
  1. Jan Tarski
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Editor information

Editors and Affiliations

  1. Institut für Theoretische Physik, Technische Universität Clausthal, 0-3392, Clausthal-Zellerfeld, Germany

    Heinz-Dietrich Doebner  & Stig I. Andersson  & 

  2. Institut für Theoretische Kernphysik, Universität Bonn, Nußallee 14-16, 0-5300, Bonn, Germany

    Herbert Rainer Petry

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© 1982 Springer-Verlag Berlin Heidelberg

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Tarski, J. (1982). Path integrals over manifolds. In: Doebner, HD., Andersson, S.I., Petry, H.R. (eds) Differential Geometric Methods in Mathematical Physics. Lecture Notes in Mathematics, vol 905. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0092440

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  • DOI: https://doi.org/10.1007/BFb0092440

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-11197-9

  • Online ISBN: 978-3-540-39002-2

  • eBook Packages: Springer Book Archive

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