The Feynman integral of quadratic potentials depending on two time variables

Kun Soo Chang, Gerald William Johnson and David Lee Skoug

Vol. 122 (1986), No. 1, 11–33

DOI: 10.2140/pjm.1986.122.11

Abstract

We show that the double integral of certain quadratic potentials depending on two time variables is in a Banach algebra 𝒮 of functions on Wiener space all of whose members have an analytic Feynman integral. Corollaries are given insuring (a) that 𝒮 contains a rather broad class of functions involving double integrals of potentials depending on two time parameters, and (b) the existence of the Fresnel integral for such functions.

Mathematical Subject Classification 2000

Primary: 28C20

Secondary: 58D20, 60H05, 81C35

Milestones

Received: 4 September 1984

Revised: 11 November 1984

Published: 1 March 1986