Pion-Pion Scattering in Chiral Perturbation and Dispersion Relation Theories

Chiral perturbation theory, the low energy effective theory of the strong interactions for the light pseudoscalar degrees of freedom, is based on effective Lagrangian techniques and is an expansion in the powers of the external momenta and the powers of the quark masses, which correct the soft-pion theorems. Our primary emphasis will be on the problem of $\pi\pi$ scattering. After briefly reviewing these features and some results, we review some features of $\pi-N$ scattering.