Generalized Zeta Functions and One-loop Corrections to Quantum Kink Masses

TL;DR

This paper develops a method using generalized zeta functions to compute one-loop quantum corrections to kink masses in various (1+1)-dimensional field theories, including sine-Gordon and sinh-Gordon models.

Contribution

It introduces a generalized zeta function regularization approach for calculating quantum kink mass corrections across multiple models.

Findings

Successfully computed one-loop corrections for sine-Gordon and sinh-Gordon kinks.

Extended the method to polynomial self-interaction models.

Provided a unified framework for quantum correction calculations.

Abstract

A method for describing the quantum kink states in the semi-classical limit of several (1+1)-dimensional field theoretical models is developed. We use the generalized zeta function regularization method to compute the one-loop quantum correction to the masses of the kink in the sine-Gordon and cubic sinh-Gordon models and another two ${\rm P}(\phi)_2$ systems with polynomial self-interactions.