The Effect of Finite Size of Composite Particles on the Casimir Energy for Scalar Field in 1+1 Dimensions

In this paper we investigate the Casimir energy for systems with the finite size of composite particles. We believe that all of the scales that naturally appear in the formulation of the problem in terms of a lagrangian and the set of boundary conditions, as internal scales. We define all other scales such as the finite size of composite particles as external scales. One of the first effects of these external scales is the restrictions could be apply on the allowed modes in the zero point energy of a system. In this paper we show how these scales (for example the finite size of composite particles) produce restrictions on the allowed modes, which alter the Casimir energy. We compare our results with those reported in the literature, which are invariably devoid of such scales, and show that the difference increases when the internal scales of the problem approach the external scales. In order to describe above effects, we use the generic and simple example of a massive scalar field confined between two points with Dirichlet boundary conditions in one spatial dimension.