Quantum corrections to the soliton mass in deformed two-dimensional models

Full text: Perturbative calculations of the quantum corrections to the soliton mass require detailed information about the spectrum of the small fluctuations around the classical soliton solution. This remains true even if the applied method does not unveil the spectral values explicitly (for example, methods based on the zeta-function regularization). Detailed spectral information is available for a few models. A suitable deformation of any of these models can produce a new model possessing soliton solutions. If the deformation is small, the properties of the fluctuations in the new model can be found by the methods of the perturbation theory. We study, at quantum level, continuous deformations of the type proposed by D. Bazeia, L. Losano and J. M. B. Malbouisson [Phys. Rev. D66 (2002) 101701(R)] for two dimensional models possessing soliton solutions. The quantum soliton survives the deformation provided the latter satisfies certain conditions. Lippmann-Schwinger equation is used in the study of the fluctuations around the soliton in the deformed model. The exceptional case when a half-bound state exists is treated in details. Under certain deformations of the model the half-bound state is transformed into a bound state. It is shown that the one-loop quantum correction to the mass of the soliton in the deformed model is given by a power series in the deformation parameter. Deformations of the sine-Gordon model and of the φ24 model are studied as examples.(author)