We introduce the notion of a “quantum structure” on an Einstein general rela- tivistic 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 classifi- cation results are analogous to those of geometric quantisation (Kostant and Souriau), but they involve the topology of spacetime, rather than the topology of the configura- tion space. We provide physically relevant examples, such as the Dirac monopole, the Aharonov–Bohm effect and the Kerr–Newman spacetime.

Quantum structures in Einstein general relativity

Vitolo, Raffaele
2000

Abstract

We introduce the notion of a “quantum structure” on an Einstein general rela- tivistic 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 classifi- cation results are analogous to those of geometric quantisation (Kostant and Souriau), but they involve the topology of spacetime, rather than the topology of the configura- tion space. We provide physically relevant examples, such as the Dirac monopole, the Aharonov–Bohm effect and the Kerr–Newman spacetime.
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11587/438791
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