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 - 10.1007/s11005-020-01331-8
DO - 10.1007/s11005-020-01331-8
M3 - Article
AN - SCOPUS:85092400272
SN - 0377-9017
VL - 110
SP - 3153
EP - 3195
JO - Letters in Mathematical Physics
JF - Letters in Mathematical Physics
IS - 12
ER -