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

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Summary

Introduction

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

Okołów
Vector spaces with scalar products
Phase space
Reduced configuration spaces
Natural variables on
An undesired property D
New variables—preliminary considerations
Summary
Preliminaries
The proof
Approaches to Quantum Gravity
Full Text
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