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Designing Dirac solutions from geometry: A light-cone blueprint via covariant relativistic dynamical inversion

Finn J. Keuchel and Andre G. Campos*

  • *Contact author: agontijo@mpi-hd.mpg.de
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Phys. Rev. A 113, 052215 – Published 14 May, 2026

DOI: https://doi.org/10.1103/b3fl-9r93

Abstract

We present a manifestly covariant route to designing exact Dirac solutions from geometric data. Given the spinor density ρ, four-velocity vμ, spin sμ, Yvon-Takabayashi (YT) angle βs, and the local Lorentz rotor, covariant relativistic dynamical inversion (CRDI) returns a real four-potential Aμ for which the prescribed spinor is a solution to the Dirac equation. We investigate the relationship between the parameters of the spinor and the electromagnetic potentials that satisfy the corresponding Dirac equation. Specifically, we examine the impact of a nontrivial variation of the YT angle and the boost matrix embedded within the spinor on the distortion of electromagnetic fields, and seek analytically tractable null-sphere solutions on the hypersurfaces u=ct−r. We show how this approach facilitates a generalized parametrization of established solutions, providing a pathway to generate novel, physically meaningful configurations.

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Phys. Rev. A 113, 052215– Published 14 May, 2026
  • Received 6 October 2025
  • Accepted 20 April 2026
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI. Open access publication funded by Max Planck Society.

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