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

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 representation 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. Finally, the U(1) invariant spinor equations, are applied to electron magnetic resonance which has many applications in the study of materials. Keywords: Weyl 2-spinor lenguage, Dirac equation, Gauge theories, Charge quantization