One-loop kink mass shifts: a computational approach

TL;DR

This paper introduces a computational method using zeta function regularization and heat kernel expansion to accurately calculate one-loop quantum corrections to kink masses in various (1+1)-dimensional scalar field models, automating the process.

Contribution

It presents a new automated algorithm for computing quantum kink mass shifts applicable to a wide range of scalar field theories, improving accuracy and versatility over previous methods.

Findings

Validated on sine-Gordon and $ ext{λ}( ext{φ})_2^4$ models with extremely low error.

Successfully applied to interpolating double sine-Gordon models.

Extended the method to analyze $ ext{φ}^6$ models.

Abstract

In this paper we develop a procedure to compute the one-loop quantum correction to the kink masses in generic (1+1)-dimensional one-component scalar field theoretical models. The procedure uses the generalized zeta function regularization method helped by the Gilkey-de Witt asymptotic expansion of the heat function via Mellin's transform. We find a formula for the one-loop kink mass shift that depends only on the part of the energy density with no field derivatives, evaluated by means of a symbolic software algorithm that automates the computation. The improved algorithm with respect to earlier work in this subject has been tested in the sine-Gordon and $\lambda(\phi)_2^4$ models. The quantum corrections of the sG-soliton and $\lambda(\phi^4)_2$-kink masses have been estimated with a relative error of 0.00006% and 0.00007% respectively. Thereafter, the algorithm is applied to other models. In particular, an interesting one-parametric family of double sine-Gordon models interpolating between the ordinary sine-Gordon and a re-scaled sine-Gordon model is addressed. Another one-parametric family, in this case of $\phi^6$ models, is analyzed. The main virtue of our procedure is its versatility: it can be applied to practically any type of relativistic scalar field models supporting kinks.