The dirac operator and gravitation

We give a brute-force proof of the fact, announced by Alain Connes, that the Wodzicki residue of the inverse square of the Dirac operator is proportional to the Einstein-Hilbert action of general relativity. We show that this also holds for twisted (e. g. by electrodynamics) Dirac operators, and more generally, for Dirac operators pertaining to Clifford connections of general Clifford bundles.