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A reasonable method for computing path integrals on curved spaces

  • Section V
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Feynman Path Integrals

Part of the book series: Lecture Notes in Physics ((LNP,volume 106))

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References

  1. In diagrammar dialect, A1 is called the two-loop contribution

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  2. 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,”

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  3. A. Truman, J. Math. Phys. 17 1852 (1976) and 18 1499 (1977).

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  4. C. DeWitt-Morette, A. Maheshwari and B. Nelson. Path Integration in Non-Relativistic quantum Mechanics. Physics Reports 1979.

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  5. For a detailed discussion see [DeWitt-Morette, Maheshwari, Nelson].

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  6. V. Volterra and B. Hostinsky. Operations Infinitesimals Lineaires. Gauthier-Villars 1938; and J. Dollard and C. N. Friedman. Product Integration. Addison-Wesley 1979.

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  7. See references quoted in [Eells and Elworthy] and [Elworthy].

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  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).

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  9. This notation gives the erroneous feeling that δY(t,x) is a small increment; it is used nevertheless for its obvious convenience.

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Author information

Authors and Affiliations

  1. Department of Astronomy and Center for Relativity, The University of Texas, 78712, Austin, Texas

    Cécile DeWitt-Morette

Authors
  1. Cécile DeWitt-Morette
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Editor information

S. Albeverio Ph. Combe R. Høegh-Krohn G. Rideau M. Sirugue-Collin M. Sirugue R. Stora

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© 1979 Springer-Verlag

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DeWitt-Morette, C. (1979). A reasonable method for computing path integrals on curved spaces. In: Albeverio, S., et al. Feynman Path Integrals. Lecture Notes in Physics, vol 106. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-09532-2_79

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  • DOI: https://doi.org/10.1007/3-540-09532-2_79

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-09532-3

  • Online ISBN: 978-3-540-35039-2

  • eBook Packages: Springer Book Archive

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