Sine-Gordon Effective Potential beyond Gaussian Approximation

TL;DR

This paper develops a method to compute the effective potential of sine-Gordon field theory beyond the Gaussian approximation, using an optimized expansion and background field method, showing improved results for certain coupling ranges.

Contribution

It introduces a novel approach combining optimized expansion and background field method to calculate the sine-Gordon effective potential beyond Gaussian approximation.

Findings

Second-order results are finite without extra renormalization for beta^2 <= 3.4 pi.

The method improves upon the Gaussian effective potential as the coupling increases.

The approach provides more accurate effective potential calculations in the specified coupling range.

Abstract

Combining an optimized expansion scheme in the spirit of the background field method with the Coleman's normal-ordering renormalization prescription, we calculate the effective potential of sine-Gordon field theory beyond the Gaussian approximation. The first-order result is just the sine-Gordon Gaussian effective potential (GEP). For the range of the coupling beta^2 <= 3.4 pi (an approximate value), a calculation with Mathematica indicates that the result up to the second order is finite without any further renormalization procedure and tends to improve the GEP more substantially while beta^2 increases from zero.