Algebraic quantum gravity (AQG): IV. Reduced phase space quantization of loop quantum gravity

By K. Giesel, T. Thiemann. 2007

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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 Brown–Kuchař mechanism in the presence of pressure-free 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 gauge-invariant 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 non-reduced 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.

Subfields: Astronomy and Astrophysics, Nuclear and High Energy Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/af03debf3c1638463a7e556b0f0b844f1bf9741c

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Citations in the corpus

Scalar material reference systems and loop quantum gravity (2012, methodology): “In section four we work out the details of the LQG quantization of the model [3] following the procedure of [17, 18, 21].”