### Abstract

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.

Original language | English (US) |
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Pages (from-to) | 880-891 |

Number of pages | 12 |

Journal | Physical Review D - Particles, Fields, Gravitation and Cosmology |

Volume | 3 |

Issue number | 4 |

DOIs | |

State | Published - 1971 |

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### ASJC Scopus subject areas

- Physics and Astronomy (miscellaneous)