Scattering theory for a class of two-particle operators of mathematical physics (the case of weak interaction)

We study the spectral properties of two-particle operators $A$ with weak interaction for spatial dimension $d\geqslant3$. We show that such an operator is unitarily equivalent to the two-particle operator $A_0$ obtained from $A$ by omitting the interaction terms. This is done using a special diagrammatic technique developed in this paper.