CASIMIR ENERGY OF A MASSIVE FIELD IN A GENUS-1 SURFACE

We review the definition of the Casimir energy stemming naturally from the concept of functional determinant through the zeta function presc ription. This is done by considering the theory at finite temperature and by defining then the Casimir energy as its energy in the limit T - -> 0. The ambiguity in the coefficient C-d/2 is understood to be a res ult of the necessary renormalization of the free energy of the system. Then, as an exact, explicit example never calculated before, the Casi mir energy for a massive scalar field living in a general (1 + 2)-dime nsional toroidal spacetime (i.e., a general surface of genus one) with fat spatial geometry - parametrized by the corresponding Teichmuller parameters - and its precise dependence on these parameters and on the mass of the field is obtained in the form of an analytic function.