QED

QED Lagrangian

  1. Full form of the QED Lagrangian
  2. Mass of the Photon field

    In the QED Lagrangian a mass term for the photon field is missing. It would have the form
    photonmassterm
    Such a mass term would spoil the local gauge invariance though. This can easily be seen since
    photonmassspoilsphaseinvariance
    Stated differently, a photon field with finite mass does not have infinite range and hence can not compensate local phase transformations in the entire space.
    As a consequence: LOCAL GAUGE INVARIANCE REQUIRES A MASSLESS PHOTON FIELD.


    The best experimental limit on the photon mass originates from measurements of Jupiter's magnetic field by Pioneer 10. Making an Ansatz for the potential of the kind
    potentialwithmass
    one obtains
    limitonphotonmass
    at 90 percent Confidence Level.


    REMARK
    A vanishing photon mass has the consequence of the transversality of electromagnetic waves:
    Without external sources and for a vanishing photon mass the electric and magnetic field fulfill wave equations
    emwaveequations
    with solutions of the form
    solutionsemwaveequations
    Since the the electric and magnetic field are divergenceless one has:
    emwavesaretransverse
  3. Intermezzo 1: P and C of the photon field
  4. Intermezzo 2: Polarisation vectors of the photon field