Abstract
The convergence of the ladder-graph series is investigated in the case of the scattering of spinless particles in the direct channel. We introduce on the space of the off-shell wave functions an appropriate Hilbert-space structure, such that the B-S integral operator is bounded in this space and the convergence of the iterative off-shell series implies the convergence on shell. These results provide a more satisfactory justification for the use of the B-S integral equation and, furthermore, the introduced formalism enables us to write the B-S equation in the Hilbert space without any change of the symmetry properties.
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