Year: 2026
Type: preprint
Abstract: We study the semiclassical limit of the Dirac equation with external electromagnetic fields using a dual formulation based on a Wasserstein-1-type distance. This distance is tailored to matrix-valued density operators and matrix-valued Wigner measures and extends earlier metrics comparing density matrices with classical phase-space distributions in the scalar case. We prove a quantitative convergence rate in the semiclassical parameter, improving previous results for the Dirac equation. Our approach relies on a Lagrange-multiplier formulation of the semiclassical limit for the full matrix-valued Wigner equation (without projection onto energy eigenspaces), introduced in [F. Golse, N. Leopold, N. Mauser, J. Möller, C. Saffirio, J. Math. Pures Appl., (2026)].
Source: arXiv (Cornell University)
Authors: Golse, François, Möller, Jakob
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Funder: Austrian Science Fund
OpenAlex ID: W7223862283