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 0264-9381/13/5/018/img1 topology yields a physically most interesting lattice within which first quantization of Dirac particles is possible. An 0264-9381/13/5/018/img2 topology also gives a lattice, but does not allow first quantized particles.
- Publication:
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Classical and Quantum Gravity
- Pub Date:
- May 1996
- DOI:
- 10.1088/0264-9381/13/5/018
- arXiv:
- arXiv:gr-qc/9601014
- Bibcode:
- 1996CQGra..13.1023T
- Keywords:
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- General Relativity and Quantum Cosmology
- E-Print:
- 23 pages Plain TeX, 3 Figures