Geodesic multiplication and quantum kinematics in a Newtonian spacetime

Details Geodesic multiplication and quantum kinematics in a Newtonian spacetime Geodesic multiplication and quantum kinematics in a Newtonian spacetime

1999-06-23

arxiv.org/abs/gr-qc/9906093v1

Webs & Quasigroups 1998-1999, ed. A. Shelekhov, Tver, 1999, pp. 127-136

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

10 pages, LaTex, submitted to "Webs and Quasigroups 1998-1999" (Tver State University, Tver)

Scientific paper

We consider a quantum test particle in the background of a Newtonian gravitational field in the framework of Cartan's formulation of nonrelativistic spacetimes. We have proposed a novel quantization of a point particle which amounts to introducing its position operators as multiplication with the corresponding Riemann normal coordinates and momentum operators as infinitesimal right translation operators determined by geodesic multiplication of points of the spacetime. We present detailed calculations for the simplest model of a two-dimensional Newtonian spacetime.

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