MASSLESS SCALAR CASIMIR EFFECT IN A CLASS OF HYPERBOLIC KALUZA-KLEIN SPACE-TIMES

In the framework of heat-kernel approach to zeta-function regularization we calculate the one-loop effective potential (Casimir effect) massless scalar field on Kaluza-Klein space-time of the form R(D-n) x H(n)/GAMMA(2 less-than-or-equal-to n < D). In addition the Selberg trace formula associated with discrete torsion-free group GAMMA of the n-dimensional Lobachevsky space H(n) is used. A negative Casimir effect related to trivial line bundle with character chi = 1 is found. A comparison of the results obtained and Casimir effect for massless field on torus backgrounds is also presented.