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arXiv · 2610.34086

The Dirac Equation in the Classical Limit: A Duality Approach to a Convergence Rate

François Golse·Jakob Möller
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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)].

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François Golse, Jakob Möller. 2026-10-25. The Dirac Equation in the Classical Limit: A Duality Approach to a Convergence Rate. https://arxiv.org/abs/2610.34086

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