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I will present some results we obtained while reviving an old approach to the S-matrix bootstrap: the Atkinson-Mandelstam method. The S-matrix bootstrap is a non-perturbative framework that uses general physical principles such as unitarity, analyticity, and crossing symmetry to constrain scattering amplitudes, which can in turn help derive bounds on observables or provide insight into strongly interacting physics.
After a pedagogical introduction to the bootstrap axioms and their motivation, I will discuss how machine learning can be used to solve unitarity as a non-linear constraint before presenting our results.