On solution spaces of massless field equations with arbitrary spin

Source abstract

The solution spaces of massless field equations ⧠ Ψ=0, with Ψ being a tensor, a (multi)spinor, or a Rarita–Schwinger field, are studied. They carry indecomposable representations of the Poincaré group whose invariant subspaces are determined. There exist indefinite invariant scalar products that allow Gupta–Bleuler quantization for all spins. For particular cases like the third–rank tensor with mixed symmetry and the Rarita–Schwinger field for spin- (3)/(2), additional field equations are discussed, which project on subspaces.