Relativistic reduction in momentum space

The Bethe-Salpeter equation is solved in momentum space in the instantaneous approximation for Lorentz vector and scalar kernels with first-order retardation corrections. Gauge dependence and retardation corrections are discussed. The lowest-order relativistic corrections are compared with the leading $v^2$/$c^2$ corrections of the coordinate-space reduction. Numerical results are given for exact Coulombic Lorentz vector and scalar potentials and compared with perturbative calculations.