I know that GR is essentially a Riemann theory w/o Torsion; the Levi-Cevita-Connection is symmetric and therefore the torsion vanishes. What happens when fermions are included? Does the spin-connection still guarantue that the covariant derivative comes with a torsion-free connection? What happens when this theory is quantized? I've never seen a QG approach talking about torsion (except for LQG where a topological term involving torsion appears; but at the same time they claim that this term does not modify the classical equations of motions) => Is there a torsion operator in LQG?