Quantization of Sine-Gordon solitons on the circle: semiclassical vs. exact results

TL;DR

This paper compares semiclassical and exact quantum results for sine-Gordon solitons on a circle, showing that semiclassical approximations remain accurate even beyond their usual regime, using zeta function regularization.

Contribution

It provides a detailed comparison between semiclassical and exact quantum calculations of sine-Gordon solitons, demonstrating the effectiveness of semiclassical methods with zeta regularization.

Findings

Excellent agreement between semiclassical and exact results

Semiclassical approximation remains accurate outside its typical regime

Uses zeta function regularization for quantum corrections

Abstract

We consider the semiclassical quantization of sine-Gordon solitons on the circle with periodic and anti-periodic boundary conditions. The 1-loop quantum corrections to the mass of the solitons are determined using zeta function regularization in the integral representation. We compare the semiclassical results with exact numerical calculations in the literature and find excellent agreement even outside the plain semiclassical regime.