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arXiv · 2010.07725

Barbero-Immirzi connections and how to build them

Andrea Orizzonte·Lorenzo Fatibene
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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.

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Andrea Orizzonte, Lorenzo Fatibene. 2020-10-15. Barbero-Immirzi connections and how to build them. https://doi.org/10.1016/j.geomphys.2021.104276

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