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

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 ${\varphi }^4$ models, we look at all possible extensions such that the kink second-order fluctuation operators are Schrödinger differential operators with Pöschl-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 ${\varphi }^4$ models.

23 pages, 4 figures, to be published in Annals of Physics

References in corpus (1)

• One-loop fluctuations of semi-local self-dual vortices

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