Correspondence of consistent and inconsistent spin-3/2 couplings via the equivalence theorem

Abstract

The Rarita-Schwinger theory of free massive spin-3/2 field obeys the physical degrees of freedom counting, and one can distinguish ``consistent'' couplings which maintain this property and ``inconsistent'' couplings which destroy it. We show how one can obtain consistent couplings from inconsistent ones by a redefinition of the spin-3/2 field. The field redefinition gives rise to additional ``contact terms'' which, via the equivalence theorem, can be associated with the contribution of the extra lower-spin degrees of freedom involved by the inconsistent coupling.