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
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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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