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Stochasticity and Quantum Chaos pp 73–90Cite as

Stochastic Representation of Quantum Dynamics

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Part of the book series: Mathematics and Its Applications ((MAIA,volume 317))

Abstract

Since the appearance of the Feynman’s paper [1] on the interpretation of quantum mechanics as a sum over classical paths there have been numerous attempts to make Feynman’s sum over paths mathematically rigorous. An approach suggested by Gelfand and Yaglom [2] to use the propagation kernel in order to construct a complex measure appeared wrong [3]. Another approach based on a Fourier transform suggested first by Ito [4] and developed by Albeverio and Hoegh-Krohn [5] defines a complex measure (Fresnel integral), which however is not supported by paths in the configuration space. A relation of such a measure to summation over polygonal paths is discussed in Elworthy and Truman [6]. There have been numerous works concerned with an analytic continuation of the Wiener integral to the Feynman integral; let us mention Cameron [3], Ito [7], Nelson [8] (see also ref. [9]).

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Author information

Authors and Affiliations

  1. Institute of Theoretical Physics, University of Wroclaw, Wroclaw, Poland

    Z. Haba

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  1. Z. Haba
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Editors and Affiliations

  1. Institute of Theoretical Physics, University of Wrocław, Wrocław, Poland

    Zbigniew Haba , Wojciech Cegła  & Lech Jakóbczyk ,  & 

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© 1995 Springer Science+Business Media Dordrecht

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Haba, Z. (1995). Stochastic Representation of Quantum Dynamics. In: Haba, Z., Cegła, W., Jakóbczyk, L. (eds) Stochasticity and Quantum Chaos. Mathematics and Its Applications, vol 317. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-0169-1_7

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  • DOI: https://doi.org/10.1007/978-94-011-0169-1_7

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-94-010-4076-1

  • Online ISBN: 978-94-011-0169-1

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