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A new classical 2-spinor approach to $U(1)$ gauge theory is presented inwhich the usual four-potential vector field is replaced by a symmetric secondrank spinor. Following a lagrangian formulation, it is shown that the four-rankspinor representing the Maxwell field tensor has a $U(1)$ local gaugeinvariance in terms of the electric and magnetic field strengths. When appliedto the magnetic field of a monopole, this formulation, via the irreduciblerepresentations condition for the gauge group, leads to a quantizationcondition differing by a factor 2 of the one predicted by Dirac without relyingon any kind of singular vector potentials.

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