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arXiv · gr-qc/9703058

Two particle Quantummechanics in 2+1 Gravity using Non Commuting Coordinates

M. Welling
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Abstract

We find that the momentum conjugate to the relative distance between two gravitating particles in their center of mass frame is a hyperbolic angle. This fact strongly suggests that momentum space should be taken to be a hyperboloid. We investigate the effect of quantization on this curved momentum space. The coordinates are represented by non commuting, Hermitian operators on this hyperboloid. We also find that there is a smallest distance between the two particles of one half times the Planck length.

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M. Welling. 1997-03-21. Two particle Quantummechanics in 2+1 Gravity using Non Commuting Coordinates. https://doi.org/10.1088/0264-9381%2F14%2F12%2F015

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