General Mathematics, Vol. 5, No. 1 - 4, pp. 199-210, 1995

Josef Janyska and Marco Modugno -- On Quantum Vector Fields in General Relativistic Quantum Mechanics

Abstract: We introduce a Lie algebra of distinguished vector fields on a quantum bundle over general relativistic classical spacetime and exhibit a natural isomorphism with the Lie algebra of quantisable functions on the classical phase space. These constructions have been inspired by analogous results in the Galilei framework related to a new quantisation scheme. The present results are expected to lead to an analogous covariant quantisation procedure in the Einstein framework.

Classification (MSC91): 53C05, 58A20, 58F06, 81S10

Keywords: Spacetime, jet, quantum bundle, quantisable functions, quantum vector fields.

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