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.
Highlights
A formulation of general relativity called Teleparallel Equivalent of General Relativity (TEGR)1 has not been yet used as a starting point for a quantization of gravity [2,3]
The kinematic quantum states in Dcorrespond to a large set of quadruplets (θ A) which have nothing to do with elements of —note that it is rather not possible for a quadruplet defining a Lorentzian metric to be a limit of a sequence of elements of
In this paper we showed that the natural variables (θ A) on the Hamiltonian configuration space of TEGR can be used to build via the general method described in [11] the space Dof kinematic quantum states
Summary
A formulation of general relativity called Teleparallel Equivalent of General Relativity (TEGR) has not been yet used as a starting point for a quantization of gravity [2,3]. Since nowadays no existing approach to quantum gravity seems to be fully successful it is worth to check whether it is possible to construct a model of quantum gravity based on TEGR. In this paper we will address an issue of constructing a space of quantum states for TEGR which could be applied in the procedure of canonical (or a canonical-like) quantization of the theory
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