Variables suitable for constructing quantum states for the Teleparallel Equivalent of General Relativity II

Abstract

We present the second (and final) part of an analysis aimed at introducing variables which are suitable for constructing a space of quantum states for the Teleparallel Equivalent of General Relativity. In the first part of the analysis we introduced a family of variables on the "position" sector of the phase space. In this paper we distinguish differentiable variables in the family. Then we define momenta conjugate to the distinguished variables and express constraints of the theory in terms of the variables and the momenta. Finally, we exclude variables which generate an obstacle for further steps of the Dirac's procedure of canonical quantization of constrained systems we are going to apply to the theory. As a result we obtain two collections of variables on the phase space which will be used (in a subsequent paper) to construct the desired space of quantum states.

35 pages, LaTeX2e

References in corpus (9)

• The teleparallel equivalent of general relativity
• Hamiltonian formulation of unimodular gravity in the teleparallel geometry
• Construction of spaces of kinematic quantum states for field theories via projective techniques
• ADM-like Hamiltonian formulation of gravity in the teleparallel geometry
• Kinematic quantum states for the Teleparallel Equivalent of General Relativity
• ADM-like Hamiltonian formulation of gravity in the teleparallel geometry: derivation of constraint algebra
• Hamiltonian formulation of a simple theory of the teleparallel geometry
• Variables suitable for constructing quantum states for the Teleparallel Equivalent of General Relativity II
• Variables suitable for constructing quantum states for the Teleparallel Equivalent of General Relativity I

Cited by in corpus (11)

• Teleparallel Gravity: From Theory to Cosmology
• Construction of spaces of kinematic quantum states for field theories via projective techniques
• ADM-like Hamiltonian formulation of gravity in the teleparallel geometry
• Kinematic quantum states for the Teleparallel Equivalent of General Relativity
• ADM-like Hamiltonian formulation of gravity in the teleparallel geometry: derivation of constraint algebra
• On Teleparallel Quantum Gravity in Schwarzschild Space-Time
• Dual loop quantizations of 3d gravity
• Variables suitable for constructing quantum states for the Teleparallel Equivalent of General Relativity II
• Space of quantum states built over metrics of fixed signature
• Constraints of the Teleparallel Equivalent of General Relativity in a gauge
• The Einstein constraints and differential forms