Electrodynamics at eleven parameters: the sixteen charges of light and the charge at its bound

@misc{reynaud2026electrodynamics,
  title = {{Electrodynamics at eleven parameters: the sixteen charges of light and the charge at its bound}},
  author = {Patrick B. Reynaud},
  howpublished = {HAL},
  year = {2026},
  month = sep,
  url = {https://hal.science/hal-05766029v2},
  note = {CC BY 4.0},
}

TY  - UNPB
TI  - Electrodynamics at eleven parameters: the sixteen charges of light and the charge at its bound
AU  - Patrick B. Reynaud
PY  - 2026
DA  - 2026/09/27
PB  - HAL
UR  - https://hal.science/hal-05766029v2
AB  - Light and charge are the two ends of one algebra. The eleven quantities of a body close in u(2, 2), the conformal algebra of Minkowski space with its centre, and Maxwell's equations are invariant under the conformal group. The free electromagnetic field therefore carries the sixteen conserved charges of the eleven: the fifteen conformal charges are the P , M , D and K blocks of the body element, and the sixteenth, the helicity, is the charge of the duality rotation, central. The paper restates these standard facts, and those of strongfield electrodynamics, in the language of the eleven, and says where the language adds a reading and where it adds nothing. The photon is a massless body. Its helicity is its one spin label, it has no position, the point and spin tensor that would give it one carrying two data the body does not have, and the momentum base of the reverse paradigm is its only base. The geometric phase of polarisation is the Wigner rotation of the composition law on the momentum sphere. Optical chirality is the sixteenth charge read locally, and magnetic helicity its analogue in a plasma; a Bose gas carries no helicity chemical potential, so the helicity of thermal light comes from its rotation and not from a potential of its own. The brightness temperature of a laser at the Schwinger intensity is 2.9 × 10 29 K, and the ceiling T P /(2π) of the thermal theory does not bound it, coherent emission being no thermal state, as the pulsar nanoshots at 10 37 to 10 41 K show. The special conformal transformations act on light as Hill's accelerated frames, with the parameter a/(2c 2 ); the algebra bounds no acceleration, and Born's field is the conformal image of Coulomb's. At the categorical bound a max = mc 3 /ℏ of a body, the force at which a static field creates pairs of it, the Rindler horizon lies at its Compton length. Gordon's metric, analogue horizons, the Cherenkov cone and photonic crystals are read as the frame body of a medium. At the charged end the Schwinger field is the electron's own field at the geometric mean of its Compton length and its classical radius, and the classical critical field E S /α lies 137 times beyond the bound, where no body goes. The maximal classical power of a body is (2α/3)(m/M P ) 2 times the Planck power; the synchrotron critical energy is 3 2 χ times the electron's energy; Sauter's length is twice the Compton length over the field in Schwinger units. Schwinger's rate at that field is 3.5 × 10 -4 pairs per Compton four-volume. Of the two readings of the bound stated by the strong-field paper, the categorical one is the series' position: the atom excludes a saturation in the Hamiltonian of a bound state, the conformal boost gives the saturation no support, and the body end then predicts nothing beyond quantum electrodynamics. What LUXE and E-320 can do is refute the dynamical reading in the coherent fields the atom does not offer. Magnetars, the muon, the proton and the string, and the electron of a laser plasma with its three temperatures close the paper.
ER  -