Lagrangian approach to the semirelativistic electron dynamics in the mean-field approximation

Abstract

We derive a mean-field model that is based on a two-component Pauli-like equation and incorporates quantum, spin, and relativistic effects up to second order in 1/c. Using a Lagrangian approach, we obtain the self-consistent charge and current densities that act as sources in the Maxwell equations. A physical interpretation is provided for the second-order corrections to the sources. The Maxwell equations are also expanded to the same order. The resulting self-consistent model constitutes a suitable semi-relativistic approximation to the full Dirac-Maxwell equations.

Phase-space methods for the spin dynamics in condensed matter systems

“…These corrections appear when one considers an expansion in 1/c of the Dirac-Maxwell equations and are consistent with the Hamiltonian of Eq. (15), as was shown recently using a Lagrangian method [32,39]. Using Eq.…”

“…A self-consistent mean-field model can further be obtained by coupling these Wigner equations to the set of Maxwell equations for the electromagnetic fields, where the sources (charge and current densities) are related to velocity moments of the Wigner function. A related mean-field model was obtained recently by Dixit et al [32] in the framework of the Schrödinger-Pauli equation.…”

Theoretical Modeling of Coherent Ultrafast Spin-Light Interactions: From One to Many-Electron Systems

“…In [6], we have derived a mean-field model that is based on a two-component Pauli-like equation and incorporates quantum, spin, and relativistic effects up to second-order in 1/c. By using a Lagrangian approach, we have obtained the selfconsistent charge and current densities that act as sources in the Maxwell equations.…”

Coherent spin-light-induced mechanisms in the semirelativistic limit of the self-consistent Dirac-Maxwell equations

“…Using the Foldy-Wouthuysen transformation, the Dirac Hamiltonian in the presence of an electromagnetic field [Eq. (1)] is expanded to second-order in 1/c (also at second-order in 1/m) [19,30,31] to give…”