Communications in Mathematical Physics

, Volume 28, Issue 1, pp 47–67

Feynman's path integral

Definition without limiting procedure
  • Cécile Morette DeWitt
Article

DOI: 10.1007/BF02099371

Cite this article as:
DeWitt, C.M. Commun.Math. Phys. (1972) 28: 47. doi:10.1007/BF02099371

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
https://static-content.springer.com/image/art%3A10.1007%2FBF02099371/MediaObjects/220_2005_BF02099371_f1.jpg
where
$$S_{\operatorname{int} } (q) = \mathop \smallint \limits_T V(q(t)) dt$$
and wheredw is a pseudomeasure whose Fourier transform is defined by
https://static-content.springer.com/image/art%3A10.1007%2FBF02099371/MediaObjects/220_2005_BF02099371_f2.jpg
for μ∈C′. Pseudomeasures are discussed; several integrals with respect to pseudomeasures are computed.

Copyright information

© Springer-Verlag 1972

Authors and Affiliations

  • Cécile Morette DeWitt
    • 1
  1. 1.Department of AstronomyUniversity of Texas at AustinUSA