Derivation of Dispersion Relations for Forward Scattering

Abstract

The dispersion relation for forward meson-nucleon scattering is derived in the simplified case of scalar neutral particles. Use is made of the local property of the nucleon field and of certain features of the mass spectrum. In addition, it is assumed that the only singularities of certain matrix elements of the nucleon field commutator are derivatives of finite order of $\delta$ functions on the light cone. Under some further assumptions of existence, the dispersion relations for the derivatives of the scattering amplitude with respect to angle at zero angle can also be derived.