, Volume 28, Issue 1, pp 47-67

Feynman's path integral

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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.

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