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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?
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?