The Dirac Equation in the Classical Limit: A Duality Approach to a Convergence Rate
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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BibTeX
@misc{golse2026dirac,
title = {{The Dirac Equation in the Classical Limit: A Duality Approach to a Convergence Rate}},
author = {François Golse and Jakob Möller},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.34086},
eprint = {2610.34086},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.34086},
}
RIS
TY - UNPB
TI - The Dirac Equation in the Classical Limit: A Duality Approach to a Convergence Rate
AU - François Golse
AU - Jakob Möller
PY - 2026
DA - 2026/10/25
PB - arXiv
DO - 10.48550/arxiv.2610.34086
UR - https://arxiv.org/abs/2610.34086
AB - 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)].
ER -