Electrodynamics in the Poincaré Gauge
In the near-field zone of matter, the dynamics of particles and field are coupled. As we have seen in previous chapters, this coupling can be described in various manners. In the covariant approach the near-field electrodynamics is considered as a coupling of transverse photons to longitudinal and scalar photons. The L- and S-photons are mutually coupled through the Lorenz gauge condition. A unitary transformation allows one to replace these last two photon types by gauge and near-field photons. From a physical point of view the presence of the L- and S-photons (or equivalently the NF- and G-photons) is not needed since all observable effects of the photons relate to the longitudinal part of the electric field. As we know, the longitudinal field is completely described in every space-time point in terms of the dynamics of the particle position variables. Up to this point we have identified the embryo state of the transverse photons with the state of the transverse part of the electromagnetic field. Although this identification may appear natural, physically it is just one choice among infinitely many other choices, which in the final analysis all lead to the same conclusion in regard to observational predictions. From a field-quantized perspective it is useful, but not necessary, to link the photon embryo to the chosen set of conjugate “position” and “momentum” variables for the electromagnetic field.