Quantum effects in softly broken gauge theories in curved space-times

The soft breaking of gauge or other symmetries is the typical Quantum Field Theory phenomenon. In many cases one can apply the Stückelberg procedure, which means introducing some additional field or fields and restore the gauge symmetry. The original softly broken theory corresponds to a particular choice of the gauge fixing condition. In this Letter we use this scheme for performing quantum calculations for some softly broken gauge theories in an arbitrary curved space-time. The following examples are treated in details: Proca field, massive QED and massive torsion coupled to fermion. Furthermore we present a qualitative discussion of the discontinuity of quantum effects in the massive spin-2 field theory, paying special attention to the similarity and differences with the massless limit in the spin-1 case.