Journal
CLASSICAL AND QUANTUM GRAVITY
Volume 22, Issue 21, Pages 4489-4513Publisher
IOP Publishing Ltd
DOI: 10.1088/0264-9381/22/21/005
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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 classical distance operator between two particles which is defined as an observable.
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