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Résumé |
In 1968, D. Atkinson proved in a series of papers the existence of functions
satisfying all known constraints of the S-matrix bootstrap for the 2-to-2 S-matrix
of scalar, gapped theories, following an approach suggested by Mandelstam.
Beyond the mathematical results themselves, the proof, based on establishing the
existence of a fixed point of a certain map, also suggests a procedure to be
implemented numerically and which would produce fully consistent S-matrix
functions via iterating dispersion relations, and using as an input a quantity
related to the inelasticity of a given scattering process.
In this talk, I will present the results of a recent paper in collaboration with
A. Zhiboedov, about the first implementation this scheme. I will first review
basic concepts of the S-matrix program, and state our working assumptions. I will
then present our numerical non-perturbative S-matrices, and discuss some of their
properties. They correspond to scalar, massive phi^4-like S-matrices in 3 and 4
dimensions, and have interesting and non-trivial high energy and near-threshold
behaviour. They also allow to make contact with the running of the coupling
constant. I will also compare to other approaches to the S-matrix bootstrap in the
literature. |
