Quantization of classically equivalent theories in superspace of simple supergravity and quantum equivalence

Theories of chiral spinor superfield and of real scalar superfield (scalar multiplet) in the external field of simple supergravity are considered. Both theories correspond to gauge theories with linearly dependent generators. The authors suggest a quantization prescription, build effective actions and prove that the theories under consideration are equivalent in a quantum sense to the theory of nonconformal chiral scalar superfield