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

G. 't Hooft
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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 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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G. 't Hooft. 1996-01-10. Quantization of Point Particles in 2+1 Dimensional Gravity and Space-Time Discreteness. https://doi.org/10.1088/0264-9381%2F13%2F5%2F018

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