New exact solutions of the Dirac equation of a charged particle interacting with an electromagnetic plane wave in a medium

Abstract

Abstract. Exact solutions are presented of the Dirac equation of a charged particle moving in a classical monochromatic electromagnetic plane wave in a medium of index of refraction n m < 1. The found solutions are expressed in terms of new complex trigonometric polynomials, which form a doubly infinite set labeled by two integer quantum numbers. These quantum numbers represent quantized spectra of the energy-momentum components of the charged particle along the polarization vector and along the propagation direction of the applied electromagnetic plane wave field (which is considered as a laser field of arbitrary high intensity propagating in an underdense plasma). The found solutions may serve as a basis for the description of possible quantum features of mechanisms of acceleration of electrons by high-intensity laser fields.

The Lagrangian formulation of strong-field quantum electrodynamics in a plasma

“…The motivation is twofold: first, it will allow us in the future to conduct cross section calculation taking the plasma effect into account. Secondly, it will prove that the dispersion relation indeed takes the massive-like form (7), as was phenomenolgically assumed in the previous articles mentioned above [23][24][25][26][27][28] . Moreover, it will provide us with a self consistent equation for the photon effective mass in strong-field waves.…”

“…Consequently, in the timelike case Schwinger pair production takes place whereas in the spacelike case bands structure is formed. Recently, specific subsets of the solutions space were obtained analytically [26][27][28] .…”

Effective photon mass and exact translating quantum relativistic structures

“…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…”

“…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.…”