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We study field models for which a quantum action (i.e. the action appearingin the generating functional of Green functions) is invariant undersupersymmetric transformations. We derive the Ward identity which is directconsequence of this invariance. We consider a change of variables in functionalintegral connected with supersymmetric transformations when its parameter isreplaced by a nilpotent functional of fields. Exact form of the correspondingJacobian is found. We find restrictions on generators of supersymmetrictransformations when a consistent quantum description of given field theoriesexists.

Supersymmetric invariant theories