Functional approach to 2+1 dimensional gravity coupled to particles

Details Functional approach to 2+1 dimensional gravity coupled to particles Functional approach to 2+1 dimensional gravity coupled to particles

2002-09-07

arxiv.org/abs/hep-th/0209061v1

Class.Quant.Grav. 20 (2003) 845-858

Physics

High Energy Physics

High Energy Physics - Theory

29 pages LaTex

Scientific paper

The quantum gravity problem of N point particles interacting with the gravitational field in 2+1 dimensions is approached working out the phase-space functional integral. The maximally slicing gauge is adopted for a non compact open universe with the topology of the plane. The conjugate momenta to the gravitational field are related to a class of meromorphic quadratic differentials. The boundary term for the non compact space is worked out in detail. In the extraction of the physical degrees of freedom functional determinants related to the puncture formulation of string theory occur and cancel out in the final reduction. Finally the ordering problem in the definition of the functional integral is discussed.

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