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arXiv · 1906.03632

A Lorentz-Covariant Interacting Electron-Photon System in One Space Dimension

Michael K. -H. Kiessling·Matthias Lienert·A. Shadi Tahvildar-Zadeh
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Abstract

A Lorenz-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 $\Psi(\mathbf{x}_{{ph}},\mathbf{x}_{{el}})$ where $\mathbf{x}_{{el}},\mathbf{x}_{{ph}}$ 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 $\{\mathbf{x}_{{el}}=\mathbf{x}_{{ph}}\}$, 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.

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Michael K. -H. Kiessling, Matthias Lienert, A. Shadi Tahvildar-Zadeh. 2019-06-09. A Lorentz-Covariant Interacting Electron-Photon System in One Space Dimension. https://doi.org/10.1007/s11005-020-01331-8

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