Proof of the Pomeranchuk Theorem and Related Theorems Deduced from Unitarity

Abstract

A new general proof of the Pomeranchuk theorem in the form of the average behavior of total cross sections is given. It contains the features of the Martin and Meiman proof and is more precise. By considering the integral of the forward amplitude, this proof can be extended to cover slowly increasing and decreasing total cross sections. The unitarity restriction on the relative behavior of particle-antiparticle total cross sections is studied in general, again without making the smoothness assumption. In particular, using unitarity, it is shown that a modified form of the Pomeranchuk theorem is valid when the total cross sections are asymptotically unbounded.