Скачать или смотреть Matthew Schwartz - Geometry and Analyticity of Scattering Amplitudes - 02-01-23

Where scattering amplitudes become singular is a key to understanding their properties, both perturbatively and non-perturbatively. A set of equations determining the location of singularities and branch points was established by Landau over 50 years ago, and shortly after a formula for the discontinuity across a branch cut starting at a given singularity was given by Cutkosky. Around the same time, an approach to studying singularities based on a geometric picture was developed by Pham. Despite the importance of this subject, there is much we still do not know. Progress in performing explicit computations and characterizing the types of functions that appear in amplitudes has inspired revisiting some old results from S-matrix theory and expanding those results for modern applications. This talk will discuss ways to think about singularities from geometric and algebraic points of view, focusing on constraints one can put on sequences of discontinuities. Such constraints will be critical to understand if we are to ever bootstrap the S-matrix using its analytic structure.