RESIDUAL MESON-MESON INTERACTION FROM LATTICE GAUGE SIMULATION IN A SIMPLE (2-DIMENSIONAL QED MODEL(1))

The residual interaction for a meson-meson system is computed utilizin g a cumulant expansion of the momentum-space time correlation matrix. The cumulant expansion serves to define free meson-meson operators. Th e definition of an effective interaction is then based on a comparison of the full (interacting) and the free (noninteracting) time correlat ion matrices. The proposed method, which may be transcribed to hadron- hadron systems in QCD, here is applied to a (2+1)-dimensional U(1) lat tice gauge model tuned such that it is confining. Fermions are treated in the staggered scheme. The effective interaction exhibits a repulsi ve core and attraction at intermediate relative distances. These findi ngs are consistent with an earlier study of the same model utilizing L uscher's method where scattering phase shifts are obtained directly. T he computed residual interaction is used to calculate scattering phase shifts, relative meson-meson wave functions, and the total cross sect ion.