Casimir energy of a massive field in a genus-1 surface

Details Casimir energy of a massive field in a genus-1 surface Casimir energy of a massive field in a genus-1 surface

1995-08-18

arxiv.org/abs/hep-th/9508086v2

Phys.Lett. B365 (1996) 72

Physics

High Energy Physics

High Energy Physics - Theory

Changes everywhere: title, abstract, contents and figures. Version to appear in Physics Letters B

Scientific paper

10.1016/0370-2693(95)01303-2

We review the definition of the Casimir energy steming naturally from the concept of functional determinant through the zeta function prescription. This is done by considering the theory at finite temperature and by defining then the Casimir energy as its energy in the limit $T\to 0$. The ambiguity in the coefficient $C_{d/2}$ is understood to be a result of the necessary renormalization of the free energy of the system. Then, as an exact, explicit example never calculated before, the Casimir energy for a massive scalar field living in a general $(1+2)$-dimensional toroidal spacetime (i.e., a general surface of genus one) with flat spatial geometry ---parametrized by the corresponding Teichm\"uller parameters--- and its precise dependence on these parameters and on the mass of the field is obtained under the form of an analytic function.

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