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

TL;DR

This paper refines variables for the phase space of Teleparallel Equivalent of General Relativity, facilitating the construction of a quantum state space by identifying suitable variables and their conjugate momenta.

Contribution

It distinguishes differentiable variables, defines their conjugate momenta, and excludes variables obstructing canonical quantization, advancing the framework for quantum gravity in teleparallel gravity.

Findings

Identified differentiable variables suitable for quantization

Defined conjugate momenta for these variables

Excluded variables that hinder Dirac's quantization procedure

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.