Quantum structures in Einstein general relativity (Q1580924)

The author presents a generalization of the geometric covariant formulation of the Galilei classical mechanics and quantum mechanics on a curved spacetime. This generalization is related to the geometric quantization. He defines an Einstein general relativistic quantum structure in analogy to the known Galilean. This new quantum structure is a Hermitian complex line bundle over spacetime endowed with a universal connection having curvature proportional to the cosymplectic form. The classification and conditions for existence of such structures are shown. They are similar to those of Kostant Souriau. A novel feature is the inclusion of the topology of the spacetime. As examples the author discusses: Minkowski spacetime, Schwarzschild spacetime, Kerr-Newman spacetime, Dirac monopole, the Aharonov-Bohm effect.