Coupled Fermion and Boson Production in a Strong Background Mean Field

Abstract. We derive quantum kinetic equations for fermion and boson production starting from a φ4 Lagrangean with minimal coupling to fermions. Decomposing the scalar field into a mean-field part and fluctuations we obtain spontaneous pair creation driven by a self-interacting strong background field. The produced fermion and boson pairs are self-consistently coupled. Consequently back reactions arise from fermion and boson currents determining the time-dependent self-interacting background mean field. We explore the numerical solution with cylindric boundary conditions for the time evolution of the mean field as well as for the number- and energy densities for fermions and bosons. We find that after a characteristic time all energy is converted from the background mean field to particle creation. Applying this general approach to the production of “quarks” and “gluons” a typical time scale for the collapse of the flux tube is 1.5 fm/c.