  There is a need for covariant solutions of bound state equations in order to
construct realistic QCD based models of mesons and baryons. Furthermore, we
ideally need to know the structure of these bound states in all kinematical
regimes, which makes a direct solution in Minkowski space (without any
3-dimensional reductions) desirable. The Bethe-Salpeter equation (BSE) for
bound states in scalar theories is reformulated and solved for arbitrary
scattering kernels in terms of a generalized spectral representation directly
in Minkowski space (K. Kusaka et al., PRD 51, 7026 '95). This differs from the
conventional Euclidean approach, where the BSE can only be solved in ladder
approximation after a Wick rotation.
