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.
Highlights
In [1] we were searching for variables on the phase space of the teleparallel equivalent of general relativity (TEGR) which are suitable for constructing a space of kinematic quantum states for the theory via projective methods described in [2]—the space of quantum states is meant to be used in a quantization of TEGR according to the Dirac’s approach to canonical quantization of constrained systems
The paper is organized as follows: in Sect. 2 we introduce basic definitions, present a precise description of the phase space of TEGR and a definition of new variables, derive some auxiliary formulae which will be used in further parts of the paper, we express the new variables in terms of the natural ones
To check for which new variables there appears an obstacle for defining quantum constraints let us first outline the projective methods [2] by means of which we would like to construct a space of kinematic quantum states for TEGR
Summary
In [1] we were searching for variables on the phase space of the teleparallel equivalent of general relativity (TEGR) which are suitable for constructing a space of kinematic quantum states for the theory via projective methods described in [2]—the space of quantum states is meant to be used in a quantization of TEGR according to the Dirac’s approach to canonical quantization of constrained systems. To describe the obstacle let us recall that according to the general construction [2] the space of quantum states would be built from some functions on the phase space called elementary degrees of freedom and in [1] we chose d.o.f. as functions naturally defined by new variables (ξιI , θ J ). 2 we introduce basic definitions, present a precise description of the phase space of TEGR and a definition of new variables (ξιI , θ J ), derive some auxiliary formulae which will be used in further parts of the paper, we express the new variables in terms of the natural ones. 6 we prove a useful lemma and in Appendix 7 we derive formulae expressing the constraints of TEGR and YMTM in terms of new variables on the phase space.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
