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We consider special supersymmetry (SUSY) transformations with $m$ generators$\overleftarrow{s}_{\alpha }$ for a certain class of models and study somephysical consequences of Grassmann-odd transformations which form an Abeliansupergroup with finite parameters and respective group-like elements beingfunctionals of field variables. The SUSY-invariant path integral measure withinconventional quantization implies the appearance, under a change of variablesrelated to such SUSY transformations, of a Jacobian which is explicitlycalculated. The Jacobian implies, first of all, the appearance of trivialinteractions in the transformed action, and, second, the presence of a modifiedWard identity which reduces to the standard Ward identities in the case ofconstant parameters. We examine the case of ${N}=1$ and $N=2$ supersymmetricharmonic oscillators to illustrate the general concept by a simple free modelwith $(1,1)$ physical degrees of freedom. It is shown that the interactionterms $U_{tr}$ have a corresponding SUSY-exact form: $U_{tr}=%\big(V_{(1)}\overleftarrow{s};V_{(2)}\overleftarrow{\bar{s}}\overleftarrow{s}%\big)$ naturally generated in this generalized formulation. We argue that thecase of non-trivial interactions cannot be obtained in such a way.

Comments on interactions in the SUSY models