An Accurate Analytical Formulation to Study the Dynamics of Soliton Relativistic Electrons in the Presence of a Photon Field
M.A. Grado-Caffaro and M. Grado-Caffaro
We treat the dynamics of soliton relativistic electrons in a photon field (which first is tackled classically) by starting from the nonlinear Dirac equation for the electrons. In fact, we derive the associated Dirac field equations by considering the corresponding Lagrangian density for minimal coupling between the Dirac field and the photon field. The total electron energy is also determined. In addition, from the above results, we elaborate an algebraic formalism to investigate rigorously and efficiently the dynamics of the aforementioned soliton relativistic electrons. Within the above formalism, the photon field is also represented as a massless Klein-Gordon field.
Keywords: Nonlinear Dirac equation; Soliton electrons; Photon field; Algebraic formalism; Klein-Gordon field.