Feynman`s path integrals and Henstock`s non-absolute integration

• Autorzy: Muldowney P.
• Języki publikacji: EN

Abstrakty

EN

R. Feynman formulated quantum mechanics in terms of integrals over spaces of paths (Feynman path integrals). But the absolute value of Feynman's integrand is not integrable. And his integrand does not generate a measure. So Lebesgue integration theory could not be used by Feynman. To establish the equivalence of his theory with the traditional formulation of quantum mechanics, Feynman gave an argument that his path integral satisfies Schrodinger's equation. This paper gives a proof of this part of Feynman's theory. To justify Feynman's and other investigators' use of the language and concepts of integration and probability theory, and to justify taking limits under the integral sign in Feynman's integral, we use R. Henstock's approach to non-absolute integration, which does not require the measure concept, and for which the absolute value of the integrand need not be integrable.

Słowa kluczowe

EN

Henstock integral; Feynman path integral; Browniam motion; Feynman-Kac formula; limits under the integral sign

PL

całka Henstocka; ścieżka całkowa Feynman`a; ruch Brownian`a; wzór Feynman-Kac; ograniczenia pod znakiem całki

• Wydawca: De Gruyter
• Czasopismo: Journal of Applied Analysis
• Rocznik: 2000
• Tom: Vol. 6, nr 1
• Strony: 1--24
• Opis fizyczny: Bibliogr. 13 poz.

Twórcy

autor

Muldowney P.

• Magee College University of Ulster Northland Road Derry BT 48 7JL North Ireland,