Three dimensional loop quantum gravity: coupling to point particles

Details Three dimensional loop quantum gravity: coupling to point particles Three dimensional loop quantum gravity: coupling to point particles

2004-02-25

arxiv.org/abs/gr-qc/0402111v2

Class.Quant.Grav. 22 (2005) 4489-4514

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

Typos corrected and references added

Scientific paper

10.1088/0264-9381/22/21/005

We consider the coupling between three dimensional gravity with zero cosmological constant and massive spinning point particles. First, we study the classical canonical analysis of the coupled system. Then, we go to the Hamiltonian quantization generalizing loop quantum gravity techniques. We give a complete description of the kinematical Hilbert space of the coupled system. Finally, we define the physical Hilbert space of the system of self-gravitating massive spinning point particles using Rovelli's generalized projection operator which can be represented as a sum over spin foam amplitudes. In addition we provide an explicit expression of the (physical) distance operator between two particles which is defined as a Dirac observable.

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