Nonperturbative approach to(Wiener) functional integral with $\phi^4$ interaction

TL;DR

This paper introduces a nonperturbative method for evaluating Wiener functional integrals with  interaction, demonstrating convergence of all infinite sums and deriving a generalized Gelfand-Yaglom equation.

Contribution

It presents a novel nonperturbative approach to compute  functional integrals, ensuring convergence and deriving a new differential equation in the continuum limit.

Findings

All infinite summations are proven to be convergent.

A generalized Gelfand-Yaglom differential equation is derived.

The method provides a nonperturbative evaluation of the  Wiener functional integral.

Abstract

We propose the another, in principe nonperturbative, method of the evaluation of the Wiener functional integral for $\phi^4$ 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.