Multispinor symmetries for massless arbitrary spin Fierz–Pauli and Rarita–Schwinger wave equations

Abstract

Massless, D( j,0)⊕D(0, j), multispinor fields of arbitrary unmixed spin j are reduced by simple matrix-algebra methods to associated tensors and tensor–spinors. A generalized Majorana condition applied to the multispinors is seen to correspond to reality and Majorana conditions on the associated tensors and tensor–spinors, respectively. The symmetries of the latter are displayed explicitly for arbitrary spin. For spin-1, - (3)/(2) , -2, and - (5)/(2) the free-field gauge-invariant Lagrangian wave equations of Maxwell (spin-1), Rarita–Schwinger (spin- (3)/(2) ), Fierz–Pauli (spin-2), and spin- (5)/(2) are derived directly and in a uniform manner from the simpler equations of the unmixed spin reps strongly suggesting the method is extendable to arbitrary spin. Similar features of massive fields are briefly reviewed.