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Path Integrals and Lie Groups

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Noncompact Lie Groups and Some of Their Applications

Part of the book series: NATO ASI Series ((ASIC,volume 429))

Abstract

The roles of Lie groups in Feynman’s path integrals in non-relativistic quantum mechanics are discussed. Dynamical as well as geometrical symmetries are found useful for path integral quantization. Two examples having the symmetry of a non-compact Lie group are considered. The first is the free quantum motion of a particle on a space of constant negative curvature. The system has a group SO (d, 1) associated with the geometrical structure, to which the technique of harmonic analysis on a homogeneous space is applied. As an example of a system having a non-compact dynamical symmetry, the (d -dimensional harmonic oscillator is chosen, which has the non-compact dynamical group SU (1,1) besides its geometrical symmetry SO (d). The radial path integral is seen as a convolution of the matrix functions of a compact group element of SU (1,1) on the continuous basis.

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Author information

Authors and Affiliations

  1. Department of Physics, State University of New York at Albany, Albany, N. Y., 12222, USA

    Akira Inomata

  2. Institut für Theoretische Physik I, Universität Erlangen-Nürnberg, Staudtstr. 7, D-91058, Erlangen, Germany

    Georg Junker

Authors
  1. Akira Inomata
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  2. Georg Junker
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Editor information

Editors and Affiliations

  1. Division of Mathematics, University of Texas, San Antonio, Texas, USA

    Elizabeth A. Tanner  & Raj Wilson  & 

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© 1994 Springer Science+Business Media Dordrecht

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Inomata, A., Junker, G. (1994). Path Integrals and Lie Groups. In: Tanner, E.A., Wilson, R. (eds) Noncompact Lie Groups and Some of Their Applications. NATO ASI Series, vol 429. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-1078-5_11

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  • DOI: https://doi.org/10.1007/978-94-011-1078-5_11

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-94-010-4470-7

  • Online ISBN: 978-94-011-1078-5

  • eBook Packages: Springer Book Archive

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