Local-Lagrangian Quantum Field Theory of Electric and Magnetic Charges

Abstract

We present a local Lagrangian density, depending on a pair of four-potentials $A$ and $B$, and charged fields ${\ensuremath{\psi}}_{n}$ with electric and magnetic charges ${e}_{n}$ and ${g}_{n}$. 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 (${e}_{n}{g}_{m}\ensuremath{-}{g}_{n}{e}_{m}$). 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 ${\ensuremath{\psi}}_{n}$ 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.