Canonical quantization of gravitating point particles in 2+1 dimensions

@article{Hooft1993CanonicalQO,
  title={Canonical quantization of gravitating point particles in 2+1 dimensions},
  author={Gerard 't Hooft},
  journal={Classical and Quantum Gravity},
  year={1993},
  volume={10},
  pages={1653-1664}
}
  • G. Hooft
  • Published 10 May 1993
  • Physics
  • Classical and Quantum Gravity
A finite number of gravitating point particles in 2+1 dimensions may close the universe they are in. A formalism previously introduced by the author using tessellated Cauchy surfaces is applied to define a quantized version of this model. Special emphasis is put on unitarity and uniqueness of the evolution operator and on the physical interpretation of the model. As far as the author knows this is the first model whose quantum version automatically discretizes time. Also spacelike distances are… 
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49 Citations
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49 Citations

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TLDR
A summary of the rather large body of work that has gone towards quantizing (2 + 1)-dimensional vacuum gravity in the setting of a spatially closed universe is summarized.
In search of fundamental discreteness in (2 + 1)-dimensional quantum gravity
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We perform canonical analysis of a model in which gravity is coupled to a spherically symmetric dust shell in 2+1 spacetime dimensions. The result is a reduced action depending on a finite number of…
The phase space structure of multi-particle models in 2+1 gravity
What can we learn about quantum gravity from a simple toy model, without actually quantizing it? The toy model consists of a finite number of point particles coupled to three-dimensional Einstein…
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In this paper we consider (2 + 1)-dimensional gravity coupled to N point particles. We introduce a gauge in which the z and components of the dreibein field become holomorphic and anti-holomorphic,…
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We study the dynamics of a massive pointlike particle coupled to gravity in four space–time dimensions. It has the same degrees of freedom as an ordinary particle: its coordinates with respect to a…
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We formulate and analyse the Hamiltonian dynamics of a pair of massive spinless point particles in. 2+1 /-dimensional Einstein gravity by anchoring the system to a conical infinity, isometric to the…
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