Algebraic quantum gravity (AQG): IV. Reduced phase space quantization of loop quantum gravity
Abstract
We perform a canonical, reduced phase space quantization of general relativity by loop quantum gravity (LQG) methods. The explicit construction of the reduced phase space is made possible by the combination of (a) the BrownKuchař mechanism in the presence of pressurefree dust fields which allows to deparametrize the theory and (b) Rovelli's relational formalism in the extended version developed by Dittrich to construct the algebra of gaugeinvariant observables. Since the resulting algebra of observables is very simple, one can quantize it using the methods of LQG. Basically, the kinematical Hilbert space of nonreduced LQG now becomes a physical Hilbert space and the kinematical results of LQG such as discreteness of spectra of geometrical operators now have physical meaning. The constraints have disappeared; however, the dynamics of the observables is driven by a physical Hamiltonian which is related to the Hamiltonian of the standard model (without dust) and which we quantize in this paper.
 Publication:

Classical and Quantum Gravity
 Pub Date:
 September 2010
 DOI:
 10.1088/02649381/27/17/175009
 arXiv:
 arXiv:0711.0119
 Bibcode:
 2010CQGra..27q5009G
 Keywords:

 General Relativity and Quantum Cosmology;
 High Energy Physics  Theory
 EPrint:
 31 pages, no figures