LEADER 04117nam 2200493 450 001 996503462903316 005 20230505151510.0 010 $a3-031-18258-8 024 7 $a10.1007/978-3-031-18258-7 035 $a(MiAaPQ)EBC7166109 035 $a(Au-PeEL)EBL7166109 035 $a(CKB)25913693000041 035 $a(DE-He213)978-3-031-18258-7 035 $a(PPN)267814313 035 $a(EXLCZ)9925913693000041 100 $a20230505d2022 uy 0 101 0 $aeng 135 $aurcnu|||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aWhat is the ie for the S-matrix? /$fHolmfridur Sigridar Hannesdottir, Sebastian Mizera 205 $a1st ed. 2022. 210 1$aCham, Switzerland :$cSpringer,$d[2022] 210 4$dİ2022 215 $a1 online resource (165 pages) 225 1 $aSpringerBriefs in Physics,$x2191-5431 311 08$aPrint version: Hannesdottir, Holmfridur Sigridar What Is the I for the S-Matrix? Cham : Springer International Publishing AG,c2023 9783031182570 320 $aIncludes bibliographical references. 327 $a1. Introduction -- 2. Unitarity implies anomalous thresholds -- 3. Primer on the analytic S-matrix 4 -- Singularities as classical saddle points -- 5. Branch cut deformations -- 6. Glimpse at generalized dispersion relations -- 7. Fluctuations around classical saddle points -- 8. Conclusion Appendix. Review of Schwinger parametrization. 330 $aThis book provides a modern perspective on the analytic structure of scattering amplitudes in quantum field theory, with the goal of understanding and exploiting consequences of unitarity, causality, and locality. It focuses on the question: Can the S-matrix be complexified in a way consistent with causality? The affirmative answer has been well understood since the 1960s, in the case of 2?2 scattering of the lightest particle in theories with a mass gap at low momentum transfer, where the S-matrix is analytic everywhere except at normal-threshold branch cuts. We ask whether an analogous picture extends to realistic theories, such as the Standard Model, that include massless fields, UV/IR divergences, and unstable particles. Especially in the presence of light states running in the loops, the traditional i? prescription for approaching physical regions might break down, because causality requirements for the individual Feynman diagrams can be mutually incompatible. We demonstrate that such analyticity problems are not in contradiction with unitarity. Instead, they should be thought of as finite-width effects that disappear in the idealized 2?2 scattering amplitudes with no unstable particles, but might persist at higher multiplicity. To fix these issues, we propose an i?-like prescription for deforming branch cuts in the space of Mandelstam invariants without modifying the analytic properties of the physical amplitude. This procedure results in a complex strip around the real part of the kinematic space, where the S-matrix remains causal. We illustrate all the points on explicit examples, both symbolically and numerically, in addition to giving a pedagogical introduction to the analytic properties of the perturbative S-matrix from a modern point of view. To help with the investigation of related questions, we introduce a number of tools, including holomorphic cutting rules, new approaches to dispersion relations, as well as formulae for local behavior of Feynman integrals near branch points. This book is well suited for anyone with knowledge of quantum field theory at a graduate level who wants to become familiar with the complex-analytic structure of Feynman integrals. 410 0$aSpringerBriefs in Physics,$x2191-5431 606 $aS-matrix theory 615 0$aS-matrix theory. 676 $a635 700 $aHannesdottir$b Holmfridur Sigridar$01273932 702 $aMizera$b Sebastian 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a996503462903316 996 $aWhat is the ie for the S-matrix$93364520 997 $aUNISA