Equations of motion as projectors and the gyromagnetic factor g_{s}=1/s} from first principles

Abstract

In this work we adopt the point of view that the equations of motion satisfied by a field are just a consequence of the representation space which the field belongs to, and the discrete symmetries we impose on it. We illustrate this view point by rederiving Dirac and Proca equations as projectors over the subspaces with well defined parity of (1/2,0)+(0,1/2) and (1/2,0)X(0,1/2) representations respectively. We formulate the equation of motion corresponding to the identification of elementary systems with states in the invariant subspaces of the squared Pauli-Lubanski operator and couple minimally to electromagnetism the corresponding equation for the (s,0)+(0,s) representation space using the gauge principle. We obtain g=1/s for particles with arbitrary spin s as conjectured by Belinfante long ago.