The Phase Space Structure of Multi Particle Models in 2+1 Gravity

Details The Phase Space Structure of Multi Particle Models in 2+1 Gravity The Phase Space Structure of Multi Particle Models in 2+1 Gravity

2001-03-23

arxiv.org/abs/gr-qc/0103084v1

Class.Quant.Grav. 18 (2001) 3497-3560

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

72 pages, LeTeX2e, 10 eps figures

Scientific paper

10.1088/0264-9381/18/17/309

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. It has finitely many physical degrees of freedom. These are basically the relative positions of the particles in spacetime and the conjugate momenta. The resulting reduced phase space is derived from Einstein gravity as a topological field theory. The crucial point is thereby that we do not make any a priori assumptions about this phase space, except that the dynamics of the gravitational field is defined by the Einstein Hilbert action. This already leads to some interesting features of the reduced phase space, such as a non-commutative structure of spacetime when the model is quantized.

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