An analytical toolkit for the S-matrix bootstrap. (English) Zbl 1461.81138
Summary: We revisit analytical methods for constraining the nonperturbative \(S\)-matrix of unitary, relativistic, gapped theories in \(d \geq 3\) 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.
MSC:
| 81U20 | \(S\)-matrix theory, etc. in quantum theory |
| 81Q10 | Selfadjoint operator theory in quantum theory, including spectral analysis |
| 81T16 | Nonperturbative methods of renormalization applied to problems in quantum field theory |
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