Canonical transformations generated by the boundary volume: Unimodular and non-Abelian teleparallel gravity

TL;DR

This paper explores how boundary volume-based canonical transformations can generate new variables in gravity theories, extending to higher dimensions and connecting to unimodular and non-Abelian teleparallel gravity frameworks.

Contribution

It demonstrates that boundary volume can serve as a generator for canonical transformations in gravity, generalizing previous three-dimensional results to higher dimensions and linking to novel gravity formulations.

Findings

Boundary volume acts as a generator for canonical transformations.

Extension of variables to dimensions greater than three.

Introduction of a non-Abelian teleparallel gravity formalism.

Abstract

Recently, a new choice of variables was identified to understand how the quantum group structure appeared in three-dimensional gravity [1]. These variables are introduced via a canonical transformation generated by a boundary term. We show that this boundary term can actually be taken to be the volume of the boundary and that the new variables can be defined in any dimension greater than three. In addition, we study the associated metric and teleparallel formalisms. The former is a variant of the Henneaux--Teitelboim model for unimodular gravity. The latter provides a non-Abelian generalization of the usual Abelian teleparallel formulation.