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On quantum vector fields in general relativistic quantum mechanics. (English) Zbl 0956.53054

The authors study a Lie algebra on a quantum bundle over a general relativistic classical spacetime, and exhibit a natural isomorphism with the Lie algebra of quantisable functions on the classical phase space. In this sense they obtain original results regarding the following topics: phase space, jet contact structure, splitting of the tangent space of spacetime, connections, gravitational objects, musical mappings, quantisable functions, quantum vector fields, complex line bundle, quantum connection etc.

MSC:

53D50 Geometric quantization
81S10 Geometry and quantization, symplectic methods
53C05 Connections (general theory)
58A20 Jets in global analysis
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