Abstract
The relation is developed between rotation generators of the Lorentz group and the magnetic fields of free-space electromagnetism. Using these classical relations, it is shown that in the quantum field theory there exists a longitudinal photomagneton, a quantized magnetic flux density operator which is directly proportional to the photon spin angular momentum. Commutation relations are given in the quantum field between the longitudinal photomagneton and the usual transverse magnetic components of quantized electromagnetism. The longitudinal component is phase free, but the transverse components are phase dependent. All three components can magnetize material in general, but only the transverse components contribute to Planck's law. The photon therefore has three, not two, relativistically invariant degrees of polarization, an axial, longitudinal, polarization, and the usual right and left circular transverse polarizations. Since the longitudinal polarization is axial, it is a phase- free magnetic field.
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Evans, M.W. The magnetic fields and rotation generators of free space electromagnetism. Found Phys 24, 1519–1542 (1994). https://doi.org/10.1007/BF02054781
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DOI: https://doi.org/10.1007/BF02054781