  In order to introduce an interaction between gravity and fermions in the
Ashtekar-Barbero-Immirzi formalism without affecting classical dynamics a
non-minimal term is necessary. The non-minimal term together with the Holst
modification to the Hilbert-Palatini action reconstruct the Nieh-Yan invariant.
As a consequence the Immirzi parameter, differently from the minimal coupling
approach, does not affect the classical dynamics, which is described by the
Einstein-Cartan action.
