Abstract
We show how to avoid the known difficulties of computing one-loop counterterms in gravitating systems with fermionic fields or some non-minimal interactions. The one-loop counter-terms and the axial anomaly are calculated for the system of coupled gravitational and Majorana spin- 1 2 fields with and without torsion. It is shown that the system is non-renormalizable in all cases. New terms containing the spinor background are found in the anomaly of the axial current. The dependence of the axial current and the axial anomaly on the gauge is studied.
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