TOPOLOGICAL CASIMIR ENERGY FOR A GENERAL-CLASS OF CLIFFORD-KLEIN SPACE-TIMES

Using zeta regularization we compute the vacuum energy for free massle ss scalar fields on ultrastatic space-times RX(Gamma/X), where X is an arbitrary noncompact irreducible rank 1 symmetric space and Gamma is a cocompact torsion free subgroup of isometries of X. The spaces X inc lude hyperbolic manifolds on which previous authors have focused. Spec ifically, using a general trace formula, we extend the work of Bytsenk o, Goncharov, Zerbini (and others), where X=SO1(m,1)/SO(m), to the oth er classical rank 1 symmetric spaces X=SU(m,1)/U(m), SP(m,1)/(SP(m)xSP (1)), and the exceptional space X = F-4(-20)/Spin(9). We find in gener al that the trivial unitary character of Gamma always induces a negati ve topological component of the energy. (C) 1997 American Institute of Physics.