The role of interaction vertices in bound state calculations

Details The role of interaction vertices in bound state calculations The role of interaction vertices in bound state calculations

2002-02-07

arxiv.org/abs/nucl-th/0202022v1

Phys.Lett. B531 (2002) 161-166

Physics

Nuclear Physics

Nuclear Theory

9 pages, 5 figures

Scientific paper

10.1016/S0370-2693(02)01362-X

In recent studies of the one and two-body Greens' 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.

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