Realization of Dirac quantization in loop quantum gravity

Abstract

The system of gravity coupled to the non-rotational dust field is studied at both classical and quantum levels. The scalar constraint of the system can be written in the form of a true physical Hamiltonian with respect to the dust time. In the framework of loop quantum gravity, the scalar constraint is promoted to a well-defined operator in a suitable Hilbert space of the coupled system, such that the physical Hamiltonian becomes a symmetric operator. By the deparametrized form, a general expression of the solutions to the quantum scalar constraint is obtained, and the observables on the space of solutions can be constructed. Moreover, the Dirac quantization procedure can be fully carried out in loop quantum gravity by this system.

6 pages

References in corpus (7)

• Gravity quantized
• Extension of loop quantum gravity to $f(R)$ theories
• Hamiltonian operator for loop quantum gravity coupled to a scalar field
• A symmetric scalar constraint for loop quantum gravity
• Quantum gravity corrections to the matter dynamics in the presence of a reference fluid
• Canonical loop quantization of the lowest-order projectable Horava gravity
• 3D gravity with dust: classical and quantum theory