Abnormal Solutions of Bethe–Salpeter Equation with Massless and Massive Exchanges

We summarize the main properties of the so called “abnormal solutions” of the Wick–Cutkosky model, i.e. two massive scalar particles interacting via massless scalar exchange (“photons”), within the Bethe–Salpeter equation. These solutions do not exist in the non-relativistic limit, in spite of having very small binding energies. They present a genuine many-body character dominated by photons, with a norm of the valence constituent wave function (two-body norm) that vanishes in the limit of zero binding energy. We present new results concerning the massive-exchange case, in particular determine under which conditions is it possible to obtain such peculiar solutions without spoiling the model by tachyonic states ( \(M^2<0\) $M^2<0$ ).