High Spins Beyond Rarita-Schwinger Framework

Original · EN

We study the eigenvalue problem of the squared Pauli-Lubanski vector, W², in the Spinor-Vector representation space and derive from it that the -s(s+1)m² subspace with s=3/2, i.e. spin 3/2 in the rest frame, is pinned down by the one sole Klein-Gordon like equation, [(p²-m²)gαᵦ-2/3pβpα- 1/3(pαγβ+pβγα) p +1/3 γα p γβ p] ψβ=0. Upon gauging this W² invariant subspace of ψμ is shown to couple to the electromagnetic field in a fully covariant fashion already at zeroth order of 1/m and with the correct gyromagnetic factor of gₛ=1/s. The gauged equation is hyperbolic and hence free from the Velo-Zwanziger problem of acausal propagation within an electromagnetic field at least to that order.