Optimized Rayleigh-Schr\"{o}dinger Expansion of the Effective Potential

TL;DR

This paper introduces an optimized Rayleigh-Schrödinger expansion method to compute the effective potential in scalar field theories beyond the Gaussian approximation, aligning with results from the functional integral approach.

Contribution

It presents a novel expansion scheme for the functional Schrödinger equation that accurately calculates the effective potential up to second order, extending beyond Gaussian approximation.

Findings

First-order result matches Gaussian effective potential.

Second-order calculation yields a post-Gaussian effective potential.

Method applied successfully to λφ^4 field theory.

Abstract

An optimized Rayleigh-Schr\"{o}dinger expansion scheme of solving the functional Schr\"odinger equation with an external source is proposed to calculate the effective potential beyond the Gaussian approximation. For a scalar field theory whose potential function has a Fourier representation in a sense of tempered distributions, we obtain the effective potential up to the second order, and show that the first-order result is just the Gaussian effective potential. Its application to the $\lambda\phi^4$ field theory yields the same post-Gaussian effective potential as obtained in the functional integral formalism.