Quantum scalar fields on anti-de Sitter space-time Original Research Article

We investigate the propagation of arbitrarily coupled scalar fields on the N-dimensional hyperbolic space HN. Using the ζ-function regularization we compute exactly the one-loop effective action. The vacuum expectation value of quadratic field fluctuations and the one-loop renormalized stress tensor are then computed using the recently proposed direct ζ-function technique. Our computation tests the validity of this approach in the presence of a continuous spectrum. Our results apply as well to the N-dimensional anti-de Sitter space-time, whose appropriate euclidean section is the hyperbolic space 0HN.