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.

arXiv comment6 pages

References in corpus (23)

• Background Independent Quantum Gravity: A Status Report
• Dust as a Standard of Space and Time in Canonical Quantum Gravity
• Fundamental Structure of Loop Quantum Gravity
• The physical hamiltonian in nonperturbative quantum gravity
• Time and a physical Hamiltonian for quantum gravity
• Algebraic Quantum Gravity (AQG) IV. Reduced Phase Space Quantisation of Loop Quantum Gravity
• Gravity quantized
• Scalar Material Reference Systems and Loop Quantum Gravity
• Prima Facie Questions in Quantum Gravity
• Extension of loop quantum gravity to $f(R)$ theories
• Loop quantum $f(R)$ theories
• Hamiltonian operator for loop quantum gravity coupled to a scalar field
• A symmetric scalar constraint for loop quantum gravity
• New Hamiltonian constraint operator for loop quantum gravity
• Time evolution in deparametrized models of loop quantum gravity
• New volume and inverse volume operators for loop quantum gravity
• Loop quantum gravity coupled to a scalar field
• $\hat{Q}$ operator for canonical quantum gravity
• Quantum gravity corrections to the matter dynamics in the presence of a reference fluid
• Towards the self-adjointness of a Hamiltonian operator in loop quantum gravity
• Canonical loop quantization of the lowest-order projectable Horava gravity
• Hamiltonian structure and connection-dynamics of Weyl gravity
• 3D gravity with dust: classical and quantum theory