Kinetics and Lagrangians of vector bosons and spinor fermions as derived from Lorentz-group invariants

Abstract This paper deals with the kinetic equations and Lagrangians of vector bosons and spinor fermions. Its goals are mainly pedagogical and methodological, and no claim of novelty is made. But the relevant equations are here derived from the fundamental Lorentz invariants, namely the two Casimir operators for a massive particle with spin-1/2 and spin-1. Special attention is paid to the chiral symmetry and its effects on the Lorentz transformation. A new road leading to the Dirac equation and its polarization spinors is thus shown. Using the spin matrices stemming from the vectorial Lorentz transformation permits one to determine directly the polarization of vector bosons and to establish their Lagrangian including these spin matrices. This approach permits one to rederive also the Maxwell equations, but more importantly to determine the origin of its spin for the massive vector boson. The kinetic helicity of the particles plays a key role in these calculations.