We treat the dynamics of colliding nuclear slabs in a relativistic quantum field theory by using the relativistic mean field approximation. Starting from Walecka's lagrangian, the nucleons are represented by single-particle spinors determined by a Dirac equation that contains a repulsive mean vector meson field and an attractive mean scalar meson field. Both fields satisfy Klein-Gordon equations whose source terms are again determined by the nucleon spinors. The two equal nuclear slabs are translationally invariant in two transverse dimensions and consist of spin and isospin symmetric nuclear matter. By specification of appropriate initial conditions for the collision, we numerically solve the system of coupled Dirac and Klein-Gordon equations for lab energies per nucleon up to 420 MeV. For small energies the results are similar to TDHF results. The time dependence of the density distribution, the mean meson fields, and the damping of the collision are studied. At the highest bombarding energy retardation effects are taken into account.