Quantization of point particles in (2 + 1)dimensional gravity and spacetime discreteness
Abstract
By investigating the canonical commutation rules for gravitating quantized particles in a (2 + 1)dimensional world, it is found that these particles live on a spacetime lattice. The spacetime lattice points can be characterized by three integers. Various representations are possible, the details depending on the topology chosen for energy  momentum space. We find that an 02649381/13/5/018/img1 topology yields a physically most interesting lattice within which first quantization of Dirac particles is possible. An 02649381/13/5/018/img2 topology also gives a lattice, but does not allow first quantized particles.
 Publication:

Classical and Quantum Gravity
 Pub Date:
 May 1996
 DOI:
 10.1088/02649381/13/5/018
 arXiv:
 arXiv:grqc/9601014
 Bibcode:
 1996CQGra..13.1023T
 Keywords:

 General Relativity and Quantum Cosmology
 EPrint:
 23 pages Plain TeX, 3 Figures