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Feynman's path integral

Definition without limiting procedure

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Abstract

Feynman's integral is defined with respect to a pseudomeasure on the space of paths: for instance, letC be the space of pathsq:T⊂ℝ → configuration space of the system, letC be the topological dual ofC; then Feynman's integral for a particle of massm in a potentialV can be written

where

$$S_{\operatorname{int} } (q) = \mathop \smallint \limits_T V(q(t)) dt$$

and wheredw is a pseudomeasure whose Fourier transform is defined by

for μ∈C′. Pseudomeasures are discussed; several integrals with respect to pseudomeasures are computed.

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Authors and Affiliations

  1. Department of Astronomy, University of Texas at Austin, USA

    Cécile Morette DeWitt

Authors
  1. Cécile Morette DeWitt
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Additional information

This work has been supported in part by a NATO Research Grant and by a National Science Foundation grant [GP-15184; GP-20033].

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DeWitt, C.M. Feynman's path integral. Commun.Math. Phys. 28, 47–67 (1972). https://doi.org/10.1007/BF02099371

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  • DOI: https://doi.org/10.1007/BF02099371

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