Energy levels of classical interacting fields in a finite domain in 1 + 1 dimensions

Abstract

We study the behaviour of bound energy levels for the case of two classical interacting fields and in a finite domain (box) in 1 + 1 dimensions upon which we impose Dirichlet boundary conditions. The total Lagrangian contains a ( /4) 4 self-interaction and an interaction term given by g 2 2 . We calculate its energy eigenfunctions and its corresponding eigenvalues and study their dependence on the size of the box (L ) as well as on the free parameters of the Lagrangian: mass ratio = M 2 /M 2 , and interaction coupling constants and g . We show that for some configurations of the above parameters, there exist critical sizes of the box for which instability points of the field appear.