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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