We present a local Lagrangian density, depending on a pair of four-potentials $A$ and $B$, and charged fields ${\psi }_n$ 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 ($e_n{g}_m-g_n{e}_m$). This condition results from the requirement that the representation of the Poincaré Lie algebra which results from Poincaré invariance, integrate to a representation of the finite Poincaré group. The finite Lorentz transformation laws of $A$, $B$, and ${\psi }_n$ 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.

Close

PrevNext

View figure in article