Charge quantization emerging from irreducible representations of the gauge group U(1) and local gauge invariance in 2-spinor lenguage

Abstract: A new classical 2-spinor approach to $U(1)$ gauge theory is presented in which the usual four-potential vector field is replaced by a symmetric second rank spinor. Following a lagrangian formulation, it is shown that the four-rank spinor representing the Maxwell field tensor has a $U(1)$ local gauge invariance in terms of the electric and magnetic field strengths. When applied to the magnetic field of a monopole, this formulation, via the irreducible representations condition for the gauge group, leads to a quantization condition differing by a factor 2 of the one predicted by Dirac without relying on any kind of singular vector potentials.