Einstein-Cartan gravity with Holst term and fermions

TL;DR

This paper explores how the ambiguity in coupling procedures affects Einstein-Cartan gravity with Holst term and fermions, providing new insights into the Immirzi parameter's physical relevance and its measurability.

Contribution

It offers a novel analysis of the coupling ambiguity's impact on the Ashtekar-Barbero-Immirzi formalism and discusses the fundamental nonuniqueness in gravity-induced fermion interactions.

Findings

Coupling ambiguity influences the physical interpretation of the Immirzi parameter.

The Immirzi parameter's measurability remains uncertain due to fundamental nonuniqueness issues.

The study clarifies the role of the Holst term in Einstein-Cartan gravity with fermions.

Abstract

We investigate the consequences of the ambiguity of minimal coupling procedure for Einstein-Cartan gravity with 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 semi--classical 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.