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Here we prove the existence and uniqueness of solutions of a class ofintegral equations describing two Dirac particles in 1+3 dimensions with directinteractions. This class of integral equations arises naturally as arelativistic generalization of the integral version of the two-particleSchr\"odinger equation. Crucial use of a multi-time wave function$\psi(x_1,x_2)$ with $x_1,x_2 \in \mathbb{R}^4$ is made. A central feature isthe time delay of the interaction. Our main result is an existence anduniqueness theorem for a Minkowski half space, meaning that Minkowski spacetimeis cut off before $t=0$. We furthermore show that the solutions are determinedby Cauchy data at the initial time; however, no Cauchy problem is admissible atother times. A second result is to extend the first one to particular FLRWspacetimes with a Big Bang singularity, using the conformal invariance of theDirac equation in the massless case. This shows that the cutoff at $t=0$ canarise naturally and be fully compatible with relativity. We thus obtain a classof interacting, manifestly covariant and rigorous models in 1+3 dimensions.

Existence of relativistic dynamics for two directly interacting Dirac particles in 1+3 dimensions