The Role of the Pauli-Lubanski Vector for the Dirac, Weyl, Proca, and Maxwell Equations

Sergey I. Kryuchkov, Nathan A. Lanfear, Sergei K. Suslov

Published 2015-10-17Version 1

We analyze basic wave equations for the classical relativistic fields, such as Dirac's equation, Weyl's two-component equation for massless neutrinos, and the Proca and Maxwell equations, from the viewpoint of the Pauli-Lubanski vector and the Casimir operators of the Poincare group. In general, in this group-theoretical approach, the above wave equations arise in certain overdetermined forms, which can be reduced to the conventional ones by a Gaussian elimination. A connection between the spin of a particle/field and consistency of the corresponding overdetermined system is established.