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 -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.
Barbero-Immirzi connections and how to build them
A. Orizzonte
First
;L. FatibeneLast
2021-01-01
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 -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.
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