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We present a local Lagrangian density, depending on a pair of four-potentials A and B, and charged fields ₍ with electric and magnetic charges e₍ and g₍. The resulting local Lagrangian field equations are equivalent to Maxwell's and Dirac's equations. The Lagrangian depends on a fixed four-vector, so manifest isotropy is lost and is regained only for quantized values of (e₍g₌-g₍e₌). This condition results from the requirement that the representation of the Poincar\'e Lie algebra which results from Poincar\'e invariance, integrate to a representation of the finite Poincar\'e group. The finite Lorentz transformation laws of A, B, and ₍ are presented here for the first time. The familiar apparatus of Lagrangian field theory is applied to yield directly the canonical commutation relations, the energy-momentum tensor, and Feynman's rules.
Daniel Zwanziger (Mon,) studied this question.