  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.
