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

One of the possible approaches to construction massive higher spin interactions is use their gauge invariant description based on introduction appropriate set Stueckelberg fields. Recently, general properties such approach were investigated by Boulanger et al (2018 J. High Energy Phys. JHEP07(2018)021). The main findings this work can be formulated in two statements. At first, there always exist enough field redefinitions bring vertex into abelian form where are some corrections transformations but algebra undeformed. second, with further (as a rule derivative) one trivially expressed terms objects free theory. Our aim show (using simple example) how these realised so-called Fradkin–Vasiliev formalism and see effects (if any) that presence massless field, hence unbroken symmetries, produce. As example we take gravitational interaction for spin-3/2 so complete investigation started Buchbinder (2014 Eur. C 74 3153) relaxing all restrictions number derivatives allowed redefinitions. We spite spin-2 first statement still valid, while vertices which not equivalent on-shell ones. Moreover, it reproduce minimal spin-3/2.