Proof of the Pomeranchuk Theorem and Related Theorems Deduced from Unitarity
- 15 November 1972
- journal article
- research article
- Published by American Physical Society (APS) in Physical Review D
- Vol. 6 (10), 2875-2883
- https://doi.org/10.1103/physrevd.6.2875
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.Keywords
This publication has 13 references indexed in Scilit:
- Upper bounds on particle-antiparticle total cross section differences at high energiesPhysics Letters B, 1970
- Polynomial behaviour of scattering amplitudes at fixed momentum transfer in theories with local observablesCommunications in Mathematical Physics, 1969
- Singular integrals, harmonic functions, and differentiability properties of functions of several variablesPublished by American Mathematical Society (AMS) ,1967
- Use of Unitarity in Proving Pomeranchuk's Theorem on Cross Sections at High EnergiesPhysical Review Letters, 1966
- Forward Scattering Amplitude and Univalent FunctionsPhysical Review B, 1965
- Number of Subtractions in Fixed-Transfer Dispersion RelationsPhysical Review B, 1964
- Connection Between the Asymptotic Behavior and the Sign of the Discontinuity in One-Dimensional Dispersion RelationsPhysical Review B, 1964
- Cross Sections at High EnergiesPhysical Review B, 1961
- Asymptotic Behavior and Subtractions in the Mandelstam RepresentationPhysical Review B, 1961
- High-Energy Limit of Scattering Cross SectionsPhysical Review Letters, 1960