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

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

1997-03-21

arxiv.org/abs/gr-qc/9703058v1

Class.Quant.Grav. 14 (1997) 3313-3326

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

18 pages Latex, 2 eps figures

Scientific paper

10.1088/0264-9381/14/12/015

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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