QG4 - Loop Quantum gravity, Quantum Geometry, Spin Foams |
Speaker_ |
Mercuri, Simone |
Talk _ |
Nieh-Yan invariant and Fermions in Ashtekar-Barbero-Immirzi formalism. |
Abstract _ |
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. |