Communications in Mathematical Physics

, Volume 28, Issue 1, pp 47–67

Feynman's path integral

Definition without limiting procedure
  • Cécile Morette DeWitt


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

© Springer-Verlag 1972

Authors and Affiliations

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

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