A Survey on Mathematical Feynman Path Integrals: Construction, Asymptotics, Applications

Albeverio, Sergio; Mazzucchi, Sonia

doi:10.1007/978-3-7643-8736-5_3

Cited by 3 publications

(2 citation statements)

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“…There have been many different mathematical ways of dealing with Feynman's ideas, so successful in modern differential geometry. The oscillatory integral approach of [1] has been updated in [3], where a more recent list of references may be found, see also [4,67]. White noise calculus is exposed in [42] with an application to Feynman path 'integrals' or distributions in Chapter 12.…”

Section: Introductionmentioning

confidence: 99%

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On Hilbert's sixth problem

Jefferies¹

2022

Preprint

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Feynman path integrals are now a standard tool in quantum physics and their use in differential geometry leads to new mathematical insights. A logical treatment of quantum phenomena seems to require a sustained mathematical analysis of path integrals. The subject is complicated by the fact that their application in flat space-time is quite different from how path integrals are used in, say, topological quantum field theory, where there is no natural notion of time translation. An historical background is given in this paper and a few mathematical approaches to Feynman path integrals in the context of nonrelativistic quantum mechanics and scalar quantum fields with polynomial self-interactions are outlined.

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Section: Introductionmentioning

confidence: 99%

“…When Henri Lebesgue published his modern theory of integration in 1904, British mathematicians, must have thought that this was another example of bizarre continental abstraction. 4 But within thirty years, G.H. Hardy, J.E.…”

Section: Introductionmentioning

confidence: 99%