Generalized Positivity Bounds On Chiral Perturbation Theory

In this dissertation we apply a new set of positivity bounds discovered recently to constrain the parameters(liand bi constants)in chiral perturbation theory up to the next-to-next-to-leading order.For the li constants,we show that the generalized positiv-ity bounds are stronger than the existing positivity bounds(Manohar-Mateu positivity bounds).For the bi constants,we show that the feasible region of these new bounds is a convex region and is enclosed for many sections of the total space.Also,we ex-plore the fundamental properties of the generalized positivity bounds with ?? scattering amplitudes calculated to two loops.We find that at low energies the analyticity is not improved by the Pade unitarization method.