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

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.