Threshold Behavior of Partial-Wave Amplitudes in Quantum Field Theory

Abstract

We show within the framework of Wightman field theory and the Haag-Ruelle scattering theory that the inelastic partial-wave amplitude for a scattering with two particles in the initial or final state has the classic threshold behavior $T\sim j^l$ and under additional assumptions the phase shifts for elastic scattering obey ${sin\delta }_l\sim k^{2l+1}$ in the low-energy limit.