Space-time resolved approach for interacting quantum field theories

An alternative approach to the usual perturbative S-matrix evaluation of quantum field theories is presented which is nonperturbative and provides full space-time resolution. We study the dynamical development of the force between two fermion wave packets for the Yukawa system. The spatial distribution of the virtual bosons that act as mediators of the force can be analyzed along with the fermionic densities. Using a potential function for the fermion-fermion interaction is a good approximation to the field theoretical calculations when the Fock space is restricted to only one boson, but in the full quantum field theory the fermion-fermion force is enhanced by higher-order multiboson processes. Furthermore, the normally attractive fermion-fermion Yukawa force can, in principle, be manipulated to even be repulsive if the momentum modes available to the virtual bosons are restricted.