The role of interaction vertices in bound state calculations

In recent studies of the one and two-body Greensʹ function for scalar interactions it was shown that crossed ladder and “crossed rainbow” (for the one-body case) exchanges play a crucial role in nonperturbative dynamics. In this Letter we use exact analytical and numerical results to show that the contribution of vertex dressings to the two-body bound state mass for scalar QED are cancelled by the self-energy and wavefunction normalization. This proves, for the first time, that the mass of a two-body bound state given by the full theory can in a very good approximation be obtained by summing only ladder and crossed ladder diagrams using a bare vertex and a constant dressed mass. We also discuss the implications of the remarkable cancellation between rainbow and crossed rainbow diagrams that is a feature of one-body calculations.