Lorentz invariance from classical particle paths in quantum field theory of electric and magnetic charge

Richard A. Brandt, Filippo Neri, Daniel Zwanziger

    Research output: Contribution to journalArticle

    Abstract

    We establish the Lorentz invariance of the quantum field theory of electric and magnetic charge. This is a priori implausible because the theory is the second-quantized version of a classical field theory which is inconsistent if the minimally coupled charged fields are smooth functions. For our proof we express the generating functional for the gauge-invariant Green's functions of quantum electrodynamics with or without magnetic charge as a path integral over the trajectories of classical charged point particles. The electric-electric and electric-magnetic interactions contribute factors exp(JDJ) and exp(JD K), where J and K are the electric and magnetic currents of classical point particles and D is the usual photon propagator. The propagator D involves the Dirac string but exp(JD K) depends on it only through a topological integer linking string and classical particle trajectories. The charge quantization condition (eigj-giej)4=integer then suffices to make the gauge-invariant Green's functions string independent. By implication, our formulation shows that if the Green's functions of quantum electrodynamics are expressed, as usual, as functional integrals over classical charged fields, the smooth field configurations have measure zero and all the support of the Feynman measure lies on the trajectories of classical point particles.

    Original languageEnglish (US)
    Pages (from-to)1153-1167
    Number of pages15
    JournalPhysical Review D - Particles, Fields, Gravitation and Cosmology
    Volume19
    Issue number4
    DOIs
    StatePublished - 1979

    Fingerprint

    electric charge
    invariance
    Green's functions
    strings
    quantum electrodynamics
    integers
    trajectories
    propagation
    particle trajectories
    electric current
    formulations
    photons
    configurations
    interactions

    ASJC Scopus subject areas

    • Physics and Astronomy (miscellaneous)

    Cite this

    Lorentz invariance from classical particle paths in quantum field theory of electric and magnetic charge. / Brandt, Richard A.; Neri, Filippo; Zwanziger, Daniel.

    In: Physical Review D - Particles, Fields, Gravitation and Cosmology, Vol. 19, No. 4, 1979, p. 1153-1167.

    Research output: Contribution to journalArticle

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    N2 - We establish the Lorentz invariance of the quantum field theory of electric and magnetic charge. This is a priori implausible because the theory is the second-quantized version of a classical field theory which is inconsistent if the minimally coupled charged fields are smooth functions. For our proof we express the generating functional for the gauge-invariant Green's functions of quantum electrodynamics with or without magnetic charge as a path integral over the trajectories of classical charged point particles. The electric-electric and electric-magnetic interactions contribute factors exp(JDJ) and exp(JD K), where J and K are the electric and magnetic currents of classical point particles and D is the usual photon propagator. The propagator D involves the Dirac string but exp(JD K) depends on it only through a topological integer linking string and classical particle trajectories. The charge quantization condition (eigj-giej)4=integer then suffices to make the gauge-invariant Green's functions string independent. By implication, our formulation shows that if the Green's functions of quantum electrodynamics are expressed, as usual, as functional integrals over classical charged fields, the smooth field configurations have measure zero and all the support of the Feynman measure lies on the trajectories of classical point particles.

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