MG11 
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Nieh-Yan invariant and Fermions in Ashtekar-Barbero-Immirzi formalism.

The Ashtekar-Barbero-Immirzi formulation of General Relativity is extended to include spinor matter fields. It is demonstrated that the consistency of the coupled system requires the introduction of a non-minimal coupling term in the action of the Dirac field. The non-minimal interaction and the Holst modification to the Hilbert-Palatini action reconstruct the Nieh-Yan invariant. Hence all the terms depending on the Immirzi parameter turn out to be encoded in the Nieh-Yan term, which reduces to a total divergence not affecting the classical dynamics. It is worth specifying that the structure of the total action allows us to split it in the self and the anti-self dual part, simplifying the calculation and the structure of the constraints.

Is Torsion a Fundamental Physical Field?

The introduction of Torsion in the framework of Einstein's theories is in general motivated by no gauge principle. But the invariance of the gravitational interaction under the group of diffeomorphisms obliges to consider not only the usual ''pure'' local Lorentz invariance but also the local rotations generated by the diff. group on the spinor bundle. This allows us to introduce two Lorentz valued connections: the spin connection and the contortion tensor. Our theory gives a gauge motivation to introduce Torsion and reduces the four-spinor interaction term of Einstein-Cartan theory to a usual vector gauge interaction.