Physics of the analytic S-matrix

You might have heard about various mathematical properties of scattering amplitudes such as analyticity, sheets, branch cuts, discontinuities, etc. What does it all mean? In these lectures, we will take a guided tour through simple scattering problems that will allow us to directly trace such properties back to physics. We will learn how different analytic features of the S-matrix are really consequences of causality, locality of interactions, unitary propagation, and so on.These notes are based on a series of lectures given in Spring 2023 at the Institute for Advanced Study in Princeton and the Higgs Centre School of Theoretical Physics in Edinburgh.(c) 2023 The Author(s). Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).