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Correspondence rules and path integrals

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Feynman Path Integrals

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

Abstract

A path-integral representation is constructed for propagators corresponding to quantum Hamiltonian operators obtained from classical Hamiltonians by an arbitrary rule of correspondence. Each rule yields a unique way of defining the path integral in the context of a formalism which does not require a limiting process. This formalism is more reliable than the usual time-slicing (lattice) definition in that all the expressions it entails are well-defined for computational purposes and it allows the explicit evaluation of large classes of path integrals. Direct substitution in the Schrödinger equation shows that there are no restrictions (such as Hermiticity or time-independence) on the Hamiltonian operator. Examples are given.

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References

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Author information

Authors and Affiliations

  1. nter for Naval Analyses of the University of Rochester, 1401 Wilson Boulevard, 22209, Arlington, Va., USA

    Maurice M. Mizrahi

Authors
  1. Maurice M. Mizrahi
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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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Mizrahi, M.M. (1979). Correspondence rules and path integrals. 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_80

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  • DOI: https://doi.org/10.1007/3-540-09532-2_80

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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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