Nonrenormalizability of the quantized Dirac-Einstein system

The coupled Dirac-Einstein system is quantized and shown to be one-loop nonrenormalizable: The diagrams with eight external fermions yield a divergence proportional to the fourth power of the fermion axial-vector current. The gravitational variables required to couple gravitation to fermions are the (sixteen) vierbein fields possessing local Lorentz as well as coordinate invariance. For gravitation coupled to bosons, the vierbein and metric formulations remain equivalent at the quantum level.