We present a local Lagrangian density, depending on a pair of four-potentials A and B, and charged fields n 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 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 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.
ASJC Scopus subject areas
- Physics and Astronomy (miscellaneous)