Nonperturbative approach to(Wiener) functional integral with ${\varphi }^4$ interaction

Abstract

We propose the another, in principe nonperturbative, method of the evaluation of the Wiener functional integral for ${\varphi }^4$ term in the action. All infinite summations in the results are proven to be convergent. We finf the "generalized" Gelfand -- Yaglom differential equation implying the functional integral in the continuum limit.

Presented at "Path integrals. From quantum information to cosmology", 8th International conference, Prague, June 6--10, 2005