Static,c-number solutions of a two dimensional sine-Gordon-like field equation

Abstract

A sine-Gordon type scalar field with a$\cos ^4 [(\sqrt {\bar \lambda } \phi )/m]$ potential in two dimensions is studied and a static,c-number, stable, finite energy solution obtained. The intersoliton potential is evaluated for this model and is shown to be long range, attractive and ‘strong’ in the weak coupling regime. A positronium-like spectrum of bound states of the soliton-antisoliton pair is derived using this potential. The coupling with a massless quark field is discussed and an exact, stable and analytic solution of the spinor field exhibiting confinement in one space dimension is obtained.