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

TL;DR

This paper explores the development of suitable variables for constructing a quantum state space in the Teleparallel Equivalent of General Relativity, addressing issues with natural variables and proposing new ones for better quantum state construction.

Contribution

It introduces a new family of variables that enable the construction of a quantum state space without undesirable properties in the teleparallel formulation of gravity.

Findings

Natural configuration variables lead to undesirable properties in quantum state space.

A new family of variables can be used to construct a better quantum state space.

The approach facilitates canonical quantization of the Teleparallel Equivalent of General Relativity.

Abstract

We present the first 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 via projective techniques - the space is meant to be applied in a canonical quantization of the theory. We show that natural configuration variables on the phase space of the theory can be used to construct a space of quantum states which however possesses an undesired property. We introduce then a family of new variables such that some elements of the family can be applied to build a space of quantum states free of that property.