A reasonable method for computing path integrals on curved spaces

  • Cécile DeWitt-Morette
Section V
Part of the Lecture Notes in Physics book series (LNP, volume 106)


Configuration Space Path Integral Curve Space Projective System Continuous Path 
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  1. [1]
    In diagrammar dialect, A1 is called the two-loop contributionGoogle Scholar
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    K. D. Elworthy, “Stochastic dynamical systems and their flows”, to appear in Proceedings of the Conference on Stochastic Analysis, Northwestern University 1978. It is hoped that the long awaited Eells and Elworthy monograph will appear soon so that their friends do not feel guilty for using the results they freely share before publication. On the other hand they should be congratulated for not publishing their work until they have made sure that their tools have no hidden defects and until they have turned it in their minds till “it has made all smooth,”Google Scholar
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    A. Truman, J. Math. Phys. 17 1852 (1976) and 18 1499 (1977).Google Scholar
  4. [4]
    C. DeWitt-Morette, A. Maheshwari and B. Nelson. Path Integration in Non-Relativistic quantum Mechanics. Physics Reports 1979.Google Scholar
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    For a detailed discussion see [DeWitt-Morette, Maheshwari, Nelson].Google Scholar
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    V. Volterra and B. Hostinsky. Operations Infinitesimals Lineaires. Gauthier-Villars 1938; and J. Dollard and C. N. Friedman. Product Integration. Addison-Wesley 1979.Google Scholar
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    See references quoted in [Eells and Elworthy] and [Elworthy].Google Scholar
  8. [8]
    As usual one identifies TbM and Rn and thinks of z either as z: T → Rn such that z(tb) = 0, or bz: T → TbM such that z(tb) = b. The metric on TbM and Rn is g(b).Google Scholar
  9. [9]
    This notation gives the erroneous feeling that δY(t,x) is a small increment; it is used nevertheless for its obvious convenience.Google Scholar

Copyright information

© Springer-Verlag 1979

Authors and Affiliations

  • Cécile DeWitt-Morette
    • 1
  1. 1.Department of Astronomy and Center for RelativityThe University of TexasAustin

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