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A Lorentz-covariant system of wave equations is formulated for aquantum-mechanical three-body system in one space dimension, comprised of onephoton and two identical massive spin one-half Dirac particles, which can bethought of as two electrons (or alternatively, two positrons). Manifestcovariance is achieved using Dirac's formalism of multi-time wave functions,i.e, wave functions$\Psi(\textbf{x}_{\text{ph}},\textbf{x}_{\text{e}_1},\textbf{x}_{\text{e}_2})$where $\textbf{x}_{\text{ph}},\textbf{x}_{\text{e}_1},\textbf{x}_{\text{e}_2}$are generic spacetime events of the photon and two electrons respectively.Their interaction is implemented via a Lorentz-invariant no-crossing-of-pathsboundary condition at the coincidence submanifolds$\{\textbf{x}_{\text{ph}}=\textbf{x}_{\text{e}_1}\}$ and$\{\textbf{x}_{\text{ph}}=\textbf{x}_{\text{e}_2}\}$ compatible withconservation of probability current. The corresponding initial-boundary valueproblem is shown to be well-posed under the additional assumption ofanti-symmetry given by the Pauli exclusion principle, and a closed-formsolution to the ensuing coupled system of Klein-Gordon and transport equationsis given.

On the relativistic quantum mechanics of a photon between two electrons in 1+1 dimensions