Field quantization in a plasma: Photon mass and charge

Abstract

It is shown here that a straightforward procedure can be used to quantize the linearized equations for an electromagnetic field in a plasma. This leads to a definition of an effective mass for the transverse photons, and a different one for the longitudinal photons, or plasmons. Both masses are simply proportional to the electron plasma density. A nonlinear perturbative analysis can also be used to extend the quantization procedure, in order to include the ponderomotive force effects. This leads to the definition of a photon charge operator. The mean value of this operator, for a quantum state with a photon occupation number equal to 1, is the equivalent charge of the photon in a plasma.

Effective photon mass and exact translating quantum relativistic structures

“…II, the charge conservation is equivalent to Q ¼ Ð drq, where the aforementioned test charge density q is given by Eq. (32). On the other hand, the energy conservation law (62) for p ¼ 0 explicitly reads…”

“…Numerous works [31][32][33][34][35][36][37][38][39][40] on the KGE assume a (right-handed) circularly polarized electromagnetic (CPEM) wave. For a monochromatic field with four-wave-vector k l ¼ ðx=c; 0; 0; kÞ, it amounts to…”

“…Although the relation between x and k could be left completely undefined, the transverse plasma dispersion relation is assumed to keep resemblance with the previous analysis in the literature. [31][32][33][34][35][36][37][38][39][40][41][42] Substitution of the Ansatz (6) into the KGE, taking into account the mass-shell condition and the dispersion relation (7), gives…”

“…32,42 Already in 1953, Anderson 43 has observed the formal analogy between the wave equations for the scalar and vector potentials in ionized media, and the evolution equations for a massive vector field. This has motivated the concept of massive Higgs boson.…”

“…Examples are provided by the analysis of the Zitterbewegung (trembling motion) of Klein-Gordon particles in extremely small spatial scales, and its simulation by classical systems, 16 the KGE as a model for the Weibel instability in relativistic quantum plasmas, 17 the description of standing EM solitons in degenerate relativistic plasmas, 18 the KGE as the starting point for the wave kinetics of relativistic quantum plasmas, 19 the KGE in the presence of a strong rotating electric field and the QED cascade, 20 the Klein-Gordon-Maxwell multistream model for quantum plasmas, 21 the negative energy waves and quantum relativistic Buneman instabilities, 22 the separation of variables of the KGE in a curved space-time in open cosmological universes, 23 the resolution of the KGE equation in the presence of Kratzer 24 and Coulombtype 25 potentials, the KGE with a short-range separable potential and interacting with an intense plane-wave EM field, 26 electrostatic one-dimensional propagating nonlinear structures and pseudo-relativistic effects on solitons in quantum semiconductor plasma, 27 the square-root KGE, 28 hot nonlinear quantum mechanics, 29 a quantum-mechanical free-electron laser model based on the single electron KGE, 30 and the inverse bremsstrahlung in relativistic quantum plasmas. Very often, the treatment of charged particle dynamics described by the Klein-Gordon or Dirac equations assumes a circularly polarized electromagnetic (CPEM) wave, [31][32][33][34][35][36][37][38][39][40] mainly due to the analytical simplicity. However, the CPEM wave is not the ideal candidate for particle confinement.…”