Quantization of Point Particles in 2+1 Dimensional Gravity and Space-Time Discreteness

Details Quantization of Point Particles in 2+1 Dimensional Gravity and Space-Time Discreteness Quantization of Point Particles in 2+1 Dimensional Gravity and Space-Time Discreteness

1996-01-10

arxiv.org/abs/gr-qc/9601014v1

Class.Quant.Grav.13:1023-1040,1996

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

23 pages Plain TeX, 3 Figures

Scientific paper

10.1088/0264-9381/13/5/018

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 space-time lattice. The space-time 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 $S_2\times S_1$ topology yields a physically most interesting lattice within which first quantization of Dirac particles is possible. An $S_3$ topology also gives a lattice, but does not allow first quantized particles.

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