Search for consistent interactions of the Rarita-Schwinger field

Abstract

Bilinear, nonderivative couplings of the massive Rarita-Schwinger (RS) field are investigated. The most general coupling of this type involves 14 $\mathrm{SL}(2, C)$ irreducible tensors. Eleven of these are considered individually and in various groups; the theory turns out to be inconsistent at both classical and quantized levels, except for a particular coupling to two vector and two scalar fields. The latter case, however, turns out to be equivalent to the free-field case, leading to the conjecture that all the consistent nonderivative "couplings" of the RS field must be equivalent to the free-field case. The analysis also shows that, for weak external fields, the same expression governs both the classical and the quantum inconsistencies for any interaction.