LEADER 00715nam0-2200265 --450 001 9910325359303321 005 20190618131651.0 100 $a20190618d1962----kmuy0itay5050 ba 101 0 $aeng 102 $aUS 105 $a 001yy 200 1 $aEero Saarinen$fby Allan Temko 210 $aLondon$cPrentice-Hall$aNew York$cG. Braziller$d1962 215 $a127 p.$cill.$d26 cm 225 1 $aMakers of contemporary architecture 610 0 $aSaarinen, Eero 676 $a720.92$v21 700 1$aTemko,$bAllan$037402 801 0$aIT$bUNINA$gREICAT$2UNIMARC 901 $aBK 912 $a9910325359303321 952 $aMTD 302$b34$fDARPU 959 $aDARPU 996 $aEero Saarinen$9296006 997 $aUNINA LEADER 00462nam 2200181z- 450 001 9910437487303321 005 20201118154834.0 035 $a(CKB)5310000000008158 035 $a(EXLCZ)995310000000008158 100 $a20200301c2018uuuu -u- - 101 0 $aeng 200 00$aIl tempo dentro le cose 210 $cAras edizioni 311 $a88-99913-56-0 906 $aBOOK 912 $a9910437487303321 996 $aIl tempo dentro le cose$92432939 997 $aUNINA LEADER 04884nam 22006855 450 001 9910739460703321 005 20251113211214.0 010 $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 $a20221229d2022 u| 0 101 0 $aeng 135 $aurcnu|||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aWhat is the i? for the S-matrix? /$fby Holmfridur Sigridar Hannesdottir, Sebastian Mizera 205 $a1st ed. 2022. 210 1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2022. 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 Feynmanintegrals 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 $aParticles (Nuclear physics) 606 $aQuantum field theory 606 $aParticles (Nuclear physics) 606 $aFunctions of complex variables 606 $aApproximation theory 606 $aElementary Particles, Quantum Field Theory 606 $aParticle Physics 606 $aFunctions of a Complex Variable 606 $aApproximations and Expansions 615 0$aParticles (Nuclear physics) 615 0$aQuantum field theory. 615 0$aParticles (Nuclear physics) 615 0$aFunctions of complex variables. 615 0$aApproximation theory. 615 14$aElementary Particles, Quantum Field Theory. 615 24$aParticle Physics. 615 24$aFunctions of a Complex Variable. 615 24$aApproximations and Expansions. 676 $a635 676 $a530.122 700 $aHannesdottir$b Holmfridur Sigridar$01273932 702 $aMizera$b Sebastian 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910739460703321 996 $aWhat is the i? for the S-matrix$94462726 997 $aUNINA