Energy Levels of Classical Interacting Fields in a Finite Domain in 1+1 Dimension

Abstract

We study the behavior of bound energy levels for the case of two classical interacting fields $ϕ$ and $χ$ in a finite domain (box) in (1 + 1) dimension on which we impose Dirichlet boundary conditions (DBC). The total Lagrangian contain a $\fracλ{4}ϕ^4$ self-interaction and an interaction term given by $g ϕ^2 χ^2$. We calculate the energy eigenfunctions and its correspondent eigenvalues and study their dependence on the size of the box (L) as well on the free parameters of the Lagrangian: mass ratio $β= \frac{M^{2}_χ}{M^{2}_ϕ}$, and interaction coupling constants $λ$ and $g$. We show that for some configurations of the above parameters, there exists critical sizes of the box for which instability points of the field $χ$ appear.