Local-Lagrangian Quantum Field Theory of Electric and Magnetic Charges

We present a local Lagrangian density, depending on a pair of four-potentials A and B, and charged fields ψₙ with electric and magnetic charges eₙ and gₙ. 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 (eₙgₘ-gₙeₘ). 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 ψₙ 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.