Title: The role of the Pauli–Lubański vector for the Dirac, Weyl, Proca, Maxwell and Fierz–Pauli equations
Abstract: We analyze basic relativistic wave equations for the classical fields, such as Dirac's equation, Weyl's two-component equation for massless neutrinos, and the Proca, Maxwell, and Fierz-Pauli 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 emphasized in the massless case.