Barbero-Immirzi connections and how to build them

Abstract

We introduce a covariant formulation of Barbero-Immirzi connections, which are used in Loop Quantum Gravity to describe gravity. We show that Barbero-Immirzi connections can be uniquely defined out of a given spin connection for any $(n+1)$-dimensional lorentzian manifold which is spin. A remarkable result is that the presence of a real Barbero-Immirzi parameter is a feature unique to the $4$-dimensional case.

arXiv comment13 pages

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Cited by in corpus (1)

• Introduction to Loop Quantum Gravity. The Holst's action and the covariant formalism