Two particle Quantummechanics in 2+1 Gravity using Non Commuting Coordinates
General Relativity and Quantum Cosmology
2009-10-30 v1
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.
Cite
@article{arxiv.gr-qc/9703058,
title = {Two particle Quantummechanics in 2+1 Gravity using Non Commuting Coordinates},
author = {M. Welling},
journal= {arXiv preprint arXiv:gr-qc/9703058},
year = {2009}
}
Comments
18 pages Latex, 2 eps figures