Functional integral with $\phi^4$ term in the action beyond standard perturbative methods II

TL;DR

This paper advances the calculation of functional integrals for anharmonic oscillators with a $\,\phi^4$ term, extending the Gelfand-Yaglom method beyond standard perturbative approaches to include correction functions.

Contribution

It provides a nonperturbative derivation of correction functions to the Gelfand-Yaglom equation for anharmonic oscillators with a quartic term.

Findings

Derived the correction function for anharmonic oscillator functional integrals.

Extended Gelfand-Yaglom method to include nonperturbative corrections.

Validated the approach through step-by-step calculations.

Abstract

To avoid problems with infinite measure, the functional integral for harmonic oscillator can be calculated by time - slicing method with continuum limit procedure proposed Gelfand and Yaglom. In previous article we proved by nonperturbative calculation the generalized Gelfand-Yaglom equation for anharmonic oscillator with positive or negative mass term. In this article we prove by step-by-step the calculation of the correction function to the Gelfand-Yaglom equation for an-harmonic oscillator.