Abstract
The vacuum energy for a free massless scalar field defined on an ultrastatic (D+1)-dimensional spacetime R*HD/ Gamma , Gamma being a torsion-free subgroup of isometries of D-dimensional Lobachevsky space HD, is explicitly computed using the Harish-Chandra-Selberg trace formula. All topologically inequivalent configurations of scalar fields are taken into account. As a result, a negative topological vacuum energy is found for a trivial line bundle related to character chi =1.
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