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.
Highlights
Quantum states are built from the representations of the symmetries, identified at the classical level
It was recently found that a canonical transformation, induced by a boundary term, could be used to have a theory defined in terms of new variables, such that the gauge symmetries do depend on the cosmological constant as well, see [20]
This provided a direct manner to retrieve the quantum group symmetries upon quantization
Summary
Quantum states are built from the representations of the symmetries, identified at the classical level. It was recently found that a canonical transformation, induced by a boundary term, could be used to have a (bulk) theory defined in terms of new variables, such that the gauge symmetries do depend on the cosmological constant as well, see [20]. This provided a direct manner to retrieve the quantum group symmetries upon quantization. We develop the notion of a gauge theory for a matched pair of Lie algebras This structure generalizes the more common semidirect product that can be found in the Poincaré case or in the decomposition of the Lorentz group in terms of rotations and boosts ( they do not form a Lie algebra).
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