H-J Matschull 2001 Class. Quantum Grav. 18 3497 doi:10.1088/0264-9381/18/17/309
H-J Matschull
Show affiliationsWhat 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. Thereby, the crucial point is that we do not make any \textit{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.
81T45 Topological field theories (See also 57R56, 58Dxx)
37J35 Completely integrable systems, topological structure of phase space, integration methods
Issue 17 (7 September 2001)
Received 20 April 2001
Published 14 August 2001
H-J Matschull 2001 Class. Quantum Grav. 18 3497
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