Einstein-Cartan gravity with Holst term and fermions

Abstract

We investigate the consequences of the ambiguity of the minimal coupling procedure for Einstein-Cartan gravity with the Holst term and fermions. A new insight is provided into the nature and physical relevance of coupling procedures considered hitherto in the context of Ashtekar-Barbero-Immirzi formalism with fermions. The issue of physical effects of the Immirzi parameter in semiclassical theory is reinvestigated. We argue that the conclusive answer to the question of its measurability will not be possible until the more fundamental problem of nonuniqueness of gravity-induced fermion interaction in Einstein-Cartan theory is solved.