Test fields on compact space-times
- 1 December 1990
- journal article
- research article
- Published by AIP Publishing in Journal of Mathematical Physics
- Vol. 31 (12) , 3064-3078
- https://doi.org/10.1063/1.528960
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.Keywords
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