Low-energy theorem for pions

Abstract

Under the assumption that incoming and outgoing pions have zero mass a gauge principle for theS-matrix is developed, leading to the generalized Adler self-consistency condition that all pion amplitudes vanish at zero pion four-momentum. In the second part the theory of composite particles is discussed from a more fundamental point of view, in connection with р-meson and low-energy\(\pi \mathcal{N}\)-scattering. A result equivalent to that of Adler and Weisberger is derived and comparison with other models discussed. The generalization to forward scattering of low-energy zero-mass pions off any target is also indicated.