Phenomenological Quantum Electrodynamics. Part II. Interaction of the Field with Charges

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Abstract
The quantization of the phenomenological field is carried through with the presence of charged particles described by a Dirac Hamiltonian. The elimination of the longitudinal field presents some features which are qualitatively different from the vacuum case. In the first place the Coulomb energy has an angular dependent term. Further the elimination procedure introduces an additional term in the interaction Hamiltonian which is proportional to the medium velocity. The physical significance of this term is clarified in the discussion of the Čerenkov radiation which is carried through in the two coordinate systems: medium at rest, particle moving and particle at rest, medium moving. The result for the total radiation emitted is in agreement with the corresponding classical calculation.