Dispersion Relations for Pion-Nucleon Scattering. I. The Spin-Flip Amplitude

Abstract

Dispersion relations are derived for the derivative with respect to $sin\vartheta$, taken at zero angle, of the spin-flip amplitude for pion-nucleon scattering. The derivation of these relations is based on general field-theoretical concepts. It is shown that the condition of microscopic causality is sufficient and essentially also necessary for the existence of these equations. The special form of the dispersion relations depends on the assumptions about the high-frequency behavior of the spin-flip amplitude.