Test fields on compact space-times

Abstract

In this paper, some basic aspects of (Lorentzian) field theory on compact Lorentz manifolds are studied. All compact space-times are acausal, i.e., possess closed timelike curves; this makes them a useful testbed in analyzing some new notions of causality that will be introduced for more general acausal space-times. In addition, studying compact space-times in their own right raises a wide range of fascinating mathematical problems some of which will be explored. It will be shown that it is reasonable to expect Lorentzian field theory on a compact space-time to provide information on the topology of the underlying manifold; if this is true, then this information is likely to be ‘‘orthogonal’’ (or complementary) to the information obtained through the study of Euclidean field theory.