Correia, MiguelSever, AmitZhiboedov, Alexander2021-04-102021-04-102021-04-102021-03-0110.1007/JHEP03(2021)013https://infoscience.epfl.ch/handle/20.500.14299/177151WOS:000625547900001We revisit analytical methods for constraining the nonperturbative S-matrix of unitary, relativistic, gapped theories in d >= 3 spacetime dimensions. We assume extended analyticity of the two-to-two scattering amplitude and use it together with elastic unitarity to develop two natural expansions of the amplitude. One is the threshold (non-relativistic) expansion and the other is the large spin expansion. The two are related by the Froissart-Gribov inversion formula. When combined with crossing and a local bound on the discontinuity of the amplitude, this allows us to constrain scattering at finite energy and spin in terms of the low-energy parameters measured in the experiment. Finally, we discuss the modern numerical approach to the S-matrix bootstrap and how it can be improved based on the results of our analysis.Physics, Particles & FieldsPhysicsscattering amplitudesnonperturbative effectsspace-time symmetriestext::journal::journal article::research article