Student Theses and Dissertations

Date of Award

1973

Document Type

Thesis

Degree Name

Doctor of Philosophy (PhD)

Thesis Advisor

Nicola Khuri

Keywords

scattering amplitudes, axiomatic field theory, pion scattering, renormalized coupling constant, dispersion relations, constructive field theory

Abstract

We investigate the problem of deriving bounds on strong interaction scattering amplitudes from the results of axiomatic field theory. The bounds on the π-π scattering amplitude at points within its analyticity domain which have been obtained by Łukaszuk and Martin are especially interesting because they contain no free parameters, and they impose absolute limits on the size of the renormalized coupling constant for π-π scattering. We improve the rigorous upper bound derived by Łukaszuk and Martin for the π⁰-π⁰ scattering amplitude at the symmetric point. Our principle new tool is the "parametric dispersion relation" of Auberson and Khuri. Also, for a ϕ⁴ type field theory with a scalar bound state which is not too tightly bound, we generalize the methods developed by Martin for π-π scattering to establish upper and lower bounds on the renormalized coupling constant and an upper bound on the physical coupling constant to the bound state. These new bounds are functions of the mass of the bound state. Numerical examples of the bound on the physical coupling constant are given for several bound state masses. Finally, we discuss the relevance of our results to constructive field theory. We point out that, while our bounds do not apply to a ϕ⁴ field theory in 1 space +1 time dimensions, they do limit the values of the renormalized coupling constant for which one could construct a ϕ⁴ field theory in 2 space +1 time (and, of course, 3 space +1 time) dimensions.

Comments

A thesis presented to the faculty of The Rockefeller University in partial fulfillment of the requirements for the degree of Doctor of Philosophy

License and Reuse Information

Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License
This work is licensed under a Creative Commons Attribution-NonCommercial-Share Alike 4.0 International License.

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