Avoiding superluminal propagation of higher spin waves via projectors onto W2 invariant subspaces

Abstract

We propose to describe higher spins as invariant subspaces of the Casimir operators of the Poincaré Group, P2, and the squared Pauli–Lubanski operator, W2, in a properly chosen representation, ψ(p) (in momentum space), of the Homogeneous Lorentz Group. The resulting equation of motion for any field with s≠0 is then just a specific combination of the respective covariant projectors. We couple minimally electromagnetism to this equation and show that the corresponding wave fronts of the classical solutions propagate causally. Furthermore, for (s,0)⊕(0,s) representations, the formalism predicts the correct gyromagnetic factor, gs=1/s. The advocated method allows us to describe any higher spin without auxiliary conditions and by one covariant matrix equation alone. This master equation is only quadratic in the momenta and its dimensionality is that of ψ(p). We prove that the suggested master equation avoids the Velo–Zwanziger problem of superluminal propagation of higher spin waves and points toward a consistent description of higher spin quantum fields.