Conformal Gravity with Dirac Matter
  Recently, we have constructed the conformal gravity with metric and torsion, finding the gravitational field equations that give the conservation laws and trace condition; in the present paper we apply this theory to the case of the Dirac matter field: we shall see that in this case the trace condition becomes trivial, but further constraints arise, which will impose severe limitations on the dynamics of such a system. 
Luca Fabbri
gr-qc hep-th math-ph math.MP