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Nonlinear Dirac equations and the electron dynamics in strong magnetic fields

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Abstract

We propose a novel class of nonlinear Dirac wave equations in \(3+1\) flat space-time dimensions. Reducing the space dimensions to 2, we study the electron dynamics in an external homogeneous magnetic field for a specific type of one-electron self-interaction providing the possible (nonlinear) ground-state Landau energy levels together with their respective eigenfunctions. We concentrate on the regime of strong magnetic fields and, thus, briefly comment on the relevance of this approach to reveal certain processes thought to occur particularly near the surfaces of magnetars.

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Acknowledgements

This work was supported by Universidad de Los Andes, Santiago, Chile, through grant FAI 12.17.

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Authors and Affiliations

  1. Complex Systems Group, Facultad de Ingenieria y Ciencias Aplicadas, Universidad de Los Andes, Santiago, Chile

    Stanley A. Bruce

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  1. Stanley A. Bruce
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Correspondence to Stanley A. Bruce.

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Bruce, S.A. Nonlinear Dirac equations and the electron dynamics in strong magnetic fields. Eur. Phys. J. Plus 136, 775 (2021). https://doi.org/10.1140/epjp/s13360-021-01750-z

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  • DOI: https://doi.org/10.1140/epjp/s13360-021-01750-z

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