On a family of (1+1)-dimensional scalar field theory models: kinks, stability, one-loop mass shifts

TL;DR

This paper introduces a family of scalar field models supporting kink solutions, allowing exact analysis of their stability and quantum mass corrections, generalizing well-known models like sine-Gordon and phi^4.

Contribution

We construct a parametric family of scalar field models with exactly solvable spectral problems, extending classical models and enabling precise stability and quantum correction calculations.

Findings

Complete stability analysis of kink solutions.

Exact computation of one-loop quantum mass shifts.

Identification of reflectionless potentials at specific parameters.

Abstract

In this paper we construct a one-parametric family of (1+1)-dimensional one-component scalar field theory models supporting kinks. Inspired by the sine-Gordon and $\phi^4$ models, we look at all possible extensions such that the kink second-order fluctuation operators are Schr\"odinger differential operators with P\"oschl-Teller potential wells. In this situation, the associated spectral problem is solvable and therefore we shall succeed in analyzing the kink stability completely and in computing the one-loop quantum correction to the kink mass exactly. When the parameter is a natural number, the family becomes the hierarchy for which the potential wells are reflectionless, the two first levels of the hierarchy being the sine-Gordon and $\phi^4$ models.