Lagrangian approach to the semi-relativistic 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.

References in corpus (1)

• From self-consistent covariant effective field theories to their Galilean-invariant counterparts

Cited by in corpus (5)

• The Schrödinger-Newton equations beyond Newton
• Semiclassical Vlasov and fluid models for an electron gas with spin effects
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• Phase-space modelling of solid-state plasmas