Author: Raffaele Vitolo

We introduce the notion of a "quantum structure" on an Einstein general relativistic classical spacetime M. It consists of a line bundle over M equipped with a connection fulfilling certain conditions.

We give a necessary and sufficient condition for the existence of quantum structures, and classify them. The existence and classification results are analogous to those of geometric quantisation (Kostant and Souriau), but they involve the topology of spacetime, rather than the topology of the configuration space. We provide physically relevant examples, as the Dirac monopole, the Aharonov-Bohm effect and the Kerr-Newman spacetime.

15 pages, LaTeX-2e (AmSLaTeX 1.2).

Published in Lett. Math. Phys. 51 (2000), 119-133.

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