Energy Levels of Interacting Fields in a Box

We study the influence of boundary conditions on energy levels of interacting fields in a box and discuss some consequences when we hange the size of the box. In order to do this we calculate the energy levels of bound states of a scalar massive field nteracting with another scalar field through the Lagrangian = > in a one-dimensional box on which we impose Dirichlet boundary conditions. We find that the gap between the bound states changes with the size of the box in a nontrivial way. For the case where the masses of the two fields are equal and for large box the energy levels of Dashen-Hasslacher-Neveu (DHN model) are recovered and we have a kind of boson condensate for the ground state. Below a critical box size the ground-state level splits, which we interpret as particle-antiparticle production under small perturbations of box size. Below other critical sizes, and , of the box, the ground state and firstexcited state merge in the continuum part of the spectrum.