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A Lorenz-covariant system of wave equations is formulated for aquantum-mechanical two-body system in one space dimension, comprised of oneelectron and one photon. Manifest Lorentz covariance is achieved using Dirac'sformalism 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 theelectron and photon, respectively. Their interaction is implemented via aLorentz-invariant no-crossing-of-paths boundary condition at the coincidencesubmanifold $\{\mathbf{x}_{{el}}=\mathbf{x}_{{ph}}\}$, compatible with particlecurrent conservation. The corresponding initial-boundary-value problem isproved to be well-posed. Electron and photon trajectories are shown to existglobally in a Hypersurface Bohm--Dirac theory, for typical particle initialconditions. Also presented are the results of some numerical experiments whichillustrate Compton scattering as well as a new phenomenon: photon capture andrelease by the electron.

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