Wave equations for spin 3/2 quantum fields

In this work, we review formulations of wave equations for spin-3/2 fields constructed from different Lorentz group representations. We analyze the Joss-Weinberg single-spin chiral representation and the double-spin chiral representation, focusing on the structure of their covariant operators. We explore the Duffin-Kemmer-Petiau (DKP) formalism and its algebraic properties, originally introduced for spin–0 and spin-1 particles, and here considered as a potential framework for spin 3/2. As a result, we recover the well-known Rarita-Schwinger representation and we find a new possibility in the $(3\mathrm{/}2,0)\oplus (0,3\mathrm{/}2)\oplus (1,1\mathrm{/}2)\oplus (1\mathrm{/}2,1)$ representation.