# 2+1 gravity and doubly special relativity

@article{Freidel200321GA, title={2+1 gravity and doubly special relativity}, author={Laurent Freidel and Jerzy Kowalski-Glikman and Lee Smolin}, journal={Physical Review D}, year={2003}, volume={69}, pages={044001} }

It is shown that gravity in 2+1 dimensions coupled to point particles provides a nontrivial example of doubly special relativity (DSR). This result is obtained by interpretation of previous results in the field and by exhibiting an explicit transformation between the phase space algebra for one particle in 2+1 gravity found by Matschull and Welling and the corresponding DSR algebra. The identification of 2+1 gravity as a DSR system answers a number of questions concerning the latter, and…

## 150 Citations

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## References

SHOWING 1-10 OF 32 REFERENCES

### Doubly special relativity and de Sitter space

- Physics, Mathematics
- 2003

In this paper we recall the construction of doubly special relativity (DSR) as a theory with energy–momentum space being the four-dimensional de Sitter space. Then the bases of the DSR theory can be…

### Quantum Mechanics of a Point Particle in 2+1 Dimensional Gravity

- Physics
- 1997

We study the phase space structure and the quantization of a pointlike particle in (2 + 1)-dimensional gravity. By adding boundary terms to the first-order Einstein-Hilbert action, and removing all…

### Striking property of the gravitational Hamiltonian.

- PhysicsPhysical review. D, Particles and fields
- 1994

The total energy of the system is non-negative, vanishing if and only if space-time is Minkowskian, and the expression provides a formula for energy per-unit length of gravitational waves with a spacelike symmetry in 3+1 dimensions.

### 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…

### The 2 + 1 Kepler problem and its quantization

- Physics
- 2001

We study a system of two pointlike particles coupled to three-dimensional Einstein gravity. The reduced phase space can be considered as a deformed version of the phase space of two…

### Canonical quantization of gravitating point particles in 2 + 1 dimensions

- Physics
- 1993

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 tesselated Cauchy surfaces is applied to…

### Non-commutative space-time of Doubly Special Relativity theories

- Physics
- 2003

Doubly Special Relativity (DSR) theory is a recently proposed theory with two observer-independent scales (of velocity and mass), which is to describe a kinematic structure underlining the theory of…

### QUANTIZATION OF POINT PARTICLES IN 2+1 DIMENSIONAL GRAVITY AND SPACE-TIME 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 space-time lattice. The space-time lattice…