2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/173376Canonical 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.17 pages; v2: new discussion of parity, more general non-minimal coupling, less details of constraint analysisGeneral Relativity and Quantum CosmologyHigh Energy Physics - Theorytext