TY - JOUR

T1 - A Lorentz-covariant interacting electron–photon system in one space dimension

AU - Kiessling, Michael K.H.

AU - Lienert, Matthias

AU - Tahvildar-Zadeh, A. Shadi

N1 - Funding Information: Thanks go also to the referees for their comments. This project has received funding from the European Union’s Framework for Research and Innovation Horizon 2020 (2014–2020) under the Marie Skłodowska-Curie Grant Agreement No. 705295. Acknowledgements Publisher Copyright: © 2020, Springer Nature B.V.

PY - 2020/12

Y1 - 2020/12

N2 - A Lorentz-covariant system of wave equations is formulated for a quantum-mechanical two-body system in one space dimension, comprised of one electron and one photon. Manifest Lorentz covariance is achieved using Dirac’s formalism of multi-time wave functions, i.e., wave functions Ψ(2)(xph,xel) where xel,xph are the generic spacetime events of the electron and photon, respectively. Their interaction is implemented via a Lorentz-invariant no-crossing-of-paths boundary condition at the coincidence submanifold {xel=xph}, compatible with particle current conservation. The corresponding initial-boundary-value problem is proved to be well-posed. Electron and photon trajectories are shown to exist globally in a hypersurface Bohm–Dirac theory, for typical particle initial conditions. Also presented are the results of some numerical experiments which illustrate Compton scattering as well as a new phenomenon: photon capture and release by the electron.

AB - A Lorentz-covariant system of wave equations is formulated for a quantum-mechanical two-body system in one space dimension, comprised of one electron and one photon. Manifest Lorentz covariance is achieved using Dirac’s formalism of multi-time wave functions, i.e., wave functions Ψ(2)(xph,xel) where xel,xph are the generic spacetime events of the electron and photon, respectively. Their interaction is implemented via a Lorentz-invariant no-crossing-of-paths boundary condition at the coincidence submanifold {xel=xph}, compatible with particle current conservation. The corresponding initial-boundary-value problem is proved to be well-posed. Electron and photon trajectories are shown to exist globally in a hypersurface Bohm–Dirac theory, for typical particle initial conditions. Also presented are the results of some numerical experiments which illustrate Compton scattering as well as a new phenomenon: photon capture and release by the electron.

KW - Compton effect

KW - Electron

KW - Multi-time wave functions

KW - Photon

KW - Relativistic quantum mechanics

KW - Two-body problem

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U2 - https://doi.org/10.1007/s11005-020-01331-8

DO - https://doi.org/10.1007/s11005-020-01331-8

M3 - Article

SN - 0377-9017

VL - 110

SP - 3153

EP - 3195

JO - Letters in Mathematical Physics

JF - Letters in Mathematical Physics

IS - 12

ER -