Canonical Gravity with Fermions

TL;DR

This paper extends canonical gravity with Ashtekar-Barbero variables to include fermions, analyzing how torsion affects the theory and implications for loop quantum gravity's parity invariance.

Contribution

It introduces a generalized framework for fermionic matter in canonical gravity and discusses necessary modifications to loop quantization.

Findings

Torsion modifies key expressions in Holst's vacuum analysis.

Loop quantum gravity's parity invariance is not manifestly preserved.

Adaptations to the classical and quantum frameworks are proposed.

Abstract

Canonical gravity in real Ashtekar-Barbero variables is generalized to allow for fermionic matter. The resulting torsion changes several expressions in Holst's original vacuum analysis, which are summarized here. This in turn requires adaptations to the known loop quantization of gravity coupled to fermions, which is discussed on the basis of the classical analysis. As a result, parity invariance is not manifestly realized in loop quantum gravity.