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arXiv · 1403.3854

Lagrangian approach to the semi-relativistic electron dynamics in the mean-field approximation

Anant Dixit·Yannick Hinschberger·Jens Zamanian·Giovanni Manfredi
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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.

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Anant Dixit, Yannick Hinschberger, Jens Zamanian, Giovanni Manfredi. 2014-03-15. Lagrangian approach to the semi-relativistic electron dynamics in the mean-field approximation. https://doi.org/10.1103/physreva.88.032117

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