# 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} }

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…

## 49 Citations

Quantization of point particles in (2+1)-dimensional gravity and spacetime discreteness

- Physics
- 1996

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…

Quantum Gravity in 2 + 1 Dimensions: The Case of a Closed Universe

- PhysicsLiving reviews in relativity
- 2005

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

- Physics
- 2009

Inspired by previous work in (2 + 1)-dimensional quantum gravity, which found evidence for a discretization of time in the quantum theory, we reexamine the issue for the case of pure Lorentzian…

Two-particle quantum mechanics in gravity using non-commuting coordinates

- Physics
- 1997

We find that the momentum conjugate to the relative distance between two gravitating particles in their centre-of-mass frame is a hyperbolic angle. This fact suggests that momentum space can be…

(2+1)-Dimensional Gravity Coupled to a Dust Shell: Quantization in Terms of Global Phase Space Variables

- PhysicsTheoretical and Mathematical Physics
- 2019

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

- Physics
- 2001

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…

Gravity in 2 + 1 dimensions as a Riemann - Hilbert problem

- Mathematics
- 1996

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,…

New approach to calculating the spectrum of a quantum space–time

- Physics
- 2017

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…

(2+1)-dimensional Einstein-Kepler problem in the centre-of-mass frame.

- Physics
- 1999

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…

## References

SHOWING 1-10 OF 11 REFERENCES

Causality in (2+1)-dimensional gravity

- Physics
- 1992

A method is presented to characterize fully the evolution of an arbitrary set of spinless particles in (unquantized) (2+1)-dimensional gravity theory. The method produces a complete series of time…

Non-perturbative 2 particle scattering amplitudes in 2+1 dimensional quantum gravity

- Physics
- 1988

A quantum theory for scalar particles interacting only gravitationally in 2+1 dimensions is considered. Since there are no real gravitons the interaction is entirely topological. Nevertheless, there…

General relativity in a (2 + 1)-dimensional space-time

- Physics
- 1984

General relativity is formulated for a (2+1)-dimensional space-time. Solutions to the vacuum field equations are locally flat. There are no gravitational waves and no Newtonian attraction between…

Einstein's theory in a three-dimensional space-time

- Physics
- 1984

As a preparation for studying quantum models, we analyze unusual features of Einstein's theory of gravitation in a three-dimensional space-time. In three dimensions, matter curves space-time only…

Classical and quantum scattering on a cone

- Physics
- 1988

The “topological” scattering of a quantized test particle in the locally flat conical geometry of a localized source in 2+1-dimensional gravity is analyzed. Wave functions and scattering amplitudes…

106; and in: ”Physics, Geometry and Topology

- Nucl. Phys
- 1988