Janyška, Joseph; Modugno, Marco On quantum vector fields in general relativistic quantum mechanics. (English) Zbl 0956.53054 Gen. Math. 5, 199-217 (1997). 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. Reviewer: Constantin Udrişte (Bucureşti) Cited in 1 Document MSC: 53D50 Geometric quantization 81S10 Geometry and quantization, symplectic methods 53C05 Connections (general theory) 58A20 Jets in global analysis Keywords:spacetime; jet; quantum bundle; quantisable function; quantum vector field PDFBibTeX XMLCite \textit{J. Janyška} and \textit{M. Modugno}, Gen. Math. 5, 199--217 (1997; Zbl 0956.53054) Full Text: EuDML