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One of the possible approaches to the construction of massive higher spininteractions is to use their gauge invariant description based on theintroduction of the appropriate set of Stueckelberg fields. Recently, thegeneral properties of such approach were investigated in [1]. The main findingsof this work can be formulated in two statements. At first, there always existenough field redefinitions to bring the vertex into abelian form where thereare some corrections to the gauge transformations but the gauge algebra isundeformed. At second, with the further (as a rule higher derivative) fieldredefinitions one can bring the vertex into trivially gauge invariant formexpressed in terms of the gauge invariant objects of the free theory.  Our aim in this work is to show (using a simple example) how these generalproperties are realised in the so-called Fradkin-Vasiliev formalism and to seethe effects (if any) that the presence of massless field, and hence of someunbroken gauge symmetries, can produce. As such example we take thegravitational interaction for massive spin-3/2 field so we complete theinvestigation started in [2] relaxing all restrictions on the number ofderivatives and allowed field redefinitions. We show that in spite of thepresence of massless spin-2 field, the first statement is still valid, whilethere exist two abelian vertices which are not equivalent on-shell to thetrivially gauge invariant ones. Moreover, it is one of this abelian verticesthat reproduce the minimal interaction for massive spin-3/2.

On massive spin-3/2 in the Fradkin-Vasiliev formalism