STEGR in Internal-Space Formulation: Formalisms, Primary Constraints, and Possible Internal Symmetries

TL;DR

This paper reformulates Symmetric Teleparallel Equivalent to General Relativity (STEGR) in an internal-space framework, exploring its formalisms, primary constraints, and potential internal symmetries, revealing two distinct symmetry possibilities.

Contribution

It introduces a new internal-space formulation of STEGR, analyzes its formalisms, and identifies two possible internal-space symmetries, expanding understanding of the theory's gauge structure.

Findings

Identified three formalisms based on vanishing-torsion property.

Discovered two possible internal-space symmetries with different breaking patterns.

Provided insights into the gauge and symmetry structure of STEGR.

Abstract

We establish the theories of Symmetric Teleparallel Equivalent to General Relativity (STEGR) in the internal-space and investigate possible internal-space symmetries among primary constraint densities in the theories. First of all, we revisit STEGR in terms of the gauge approach to gravity and formulate it in the internal-space set-up. We find three possible formalisms according to the vanishing-torsion property. Then, we investigate possible internal-space symmetries in each formalism. We find that in our formulation there are two possible symmetries. One satisfies the translation symmetry but broken in the local symmetry provided by the general linear group which contains the local Lorentz symmetry. The other satisfies the latter symmetry but is absent in the former symmetry. Finally, we conclude this work and show future perspectives.