In recent studies of the one and two-body problem 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 wavefunction normalization. This proves, for the first time, that the mass of a two-body bound state given by the full theory can 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.

Authors: Cetin Savkli, Franz Gross, John Tjon

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