Massless Wigner particles in conformal field theory are free (Q2879434)

The article uses the operator-algebraic approach of Haag und Kastler and studies conformal field theory in four spacetime dimensions. Many years ago, Detlev Buchholz and Klaus Fredenhagen already proved that the S-matrix of a dilatation-invariant theory is trivial. There is no interaction. Also within the Wightman formulation any dilatation-invariant scalar field under the assumption of asymptotic completeness is a free field. The assumptions in this article are stronger, since conformal invariance is assumed. Clearly, within the framework of Haag-Kastler, one does assume neither the existence of a Wightman formulation nor asymptotic completeness. Also the whole approach is non-perturbative. If the massless particles are scalar, it is shown that the free field subnet decouples as a tensor product. Therefore, massless particles cannot interact in conformal field theory.