2004/07/15 by Mariana Kirchbach, Kirchbach, Mariana, Mauro Napsuciale +1
Physics and Astronomy · #FOS: Physical sciences #High Energy Physics - Phenomenology (hep-ph) #hep-ph
paper · pdf · doi:10.48550/arxiv.hep-ph/0407179
16 pages, revised version
arxiv created 2005/05/27 · arxiv updated 2009/12/01
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)\not p +1/3 γα\not p γβ\not 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.