Analytic Properties Of Feynman Integrals For Scattering Amplitudes
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Analytic Properties Of Feynman Integrals For Scattering Amplitudes
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Author : Pascal Wasser
language : en
Publisher:
Release Date : 2018
Analytic Properties Of Feynman Integrals For Scattering Amplitudes written by Pascal Wasser and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018 with categories.
Analytic Properties Of Feynman Diagrams In Quantum Field Theory
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Author : I. T. Todorov
language : en
Publisher: Elsevier
Release Date : 2014-05-17
Analytic Properties Of Feynman Diagrams In Quantum Field Theory written by I. T. Todorov and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-05-17 with Science categories.
Analytic Properties of Feynman Diagrams in Quantum Field Theory deals with quantum field theory, particularly in the study of the analytic properties of Feynman graphs. This book is an elementary presentation of a self-contained exposition of the majorization method used in the study of these graphs. The author has taken the intermediate position between Eden et al. who assumes the physics of the analytic properties of the S-matrix, containing physical ideas and test results without using the proper mathematical methods, and Hwa and Teplitz, whose works are more mathematically inclined with applications of algebraic topology and homology theory. The book starts with the definition of the quadratic form of a Feynman diagram, and then explains the majorization of Feynman diagrams. The book describes the derivation of spectral representations, the dispersion relations for the nucleon-nucleon scattering amplitude, and for the corresponding partial wave amplitude. The text then analyzes the surface of singularities of a Feynman diagram with notes explaining the Cutkosky rules of the Mandelstam representation for the box diagram. This text is ideal for mathematicians, physicists dealing with quantum theory and mechanics, students, and professors in advanced mathematics.
Modern Analytic Methods For Computing Scattering Amplitudes
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Author : Simone Zoia
language : en
Publisher: Springer Nature
Release Date : 2022-05-18
Modern Analytic Methods For Computing Scattering Amplitudes written by Simone Zoia and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-05-18 with Science categories.
This work presents some essential techniques that constitute the modern strategy for computing scattering amplitudes. It begins with an introductory chapter to fill the gap between a standard QFT course and the latest developments in the field. The author then tackles the main bottleneck: the computation of the loop Feynman integrals. The most efficient technique for their computation is the method of the differential equations. This is discussed in detail, with a particular focus on the mathematical aspects involved in the derivation of the differential equations and their solution. Ample space is devoted to the special functions arising from the differential equations, to their analytic properties, and to the mathematical techniques which allow us to handle them systematically. The thesis also addresses the application of these techniques to a cutting-edge problem of importance for the physics programme of the Large Hadron Collider: five-particle amplitudes at two-loop order. It presents the first analytic results for complete two-loop five-particle amplitudes, in supersymmetric theories and QCD. The techniques discussed here open the door to precision phenomenology for processes of phenomenological interest, such as three-photon, three-jet, and di-photon + jet production.
What Is The I For The S Matrix
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Author : Holmfridur Sigridar Hannesdottir
language : en
Publisher: Springer Nature
Release Date : 2023-01-01
What Is The I For The S Matrix written by Holmfridur Sigridar Hannesdottir and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-01-01 with Science categories.
This 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 iε 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 iε-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.
Analytic Properties And Bounds Of The Scattering Amplitudes
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Author : André Martin
language : en
Publisher:
Release Date : 1970
Analytic Properties And Bounds Of The Scattering Amplitudes written by André Martin and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1970 with categories.
Scattering In Quantum Field Theories
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Author : Daniel Iagolnitzer
language : en
Publisher: Princeton University Press
Release Date : 2014-07-14
Scattering In Quantum Field Theories written by Daniel Iagolnitzer and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-07-14 with Science categories.
Axiomatic and constructive approaches to quantum field theory first aim to establish it on precise, non-perturbative bases: general axioms and rigorous definition of specific theories respectively. From the viewpoint of particle physics, the goal is then to develop a relativistic scattering theory, including particle analysis and the derivation of general properties of collision amplitudes. Taking into account successive improvements, this book provides a modern, self-contained, and coherent presentation of important developments from the last twenty years, most of which have not been treated or discussed in detail in earlier books. These developments include in particular the axiomatic derivation, in massive theories, of general causal and momentum-space analyticity properties of multiparticle collision amplitudes; the constructive definition, initially in the (unphysical) euclidean space, of various models including non-super-renormalizable theories treated in the 1980s via phase-space expansions; and the subsequent constructive approach to scattering theory, which provides information on the mass spectrum, asymptotic completeness, and multiparticle structure in increasingly higher energy regions. Originally published in 1993. The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.
Generalized Feynman Amplitudes Am 62 Volume 62
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Author : Eugene R. Speer
language : en
Publisher: Princeton University Press
Release Date : 2016-03-02
Generalized Feynman Amplitudes Am 62 Volume 62 written by Eugene R. Speer and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-03-02 with Mathematics categories.
This book contains a valuable discussion of renormalization through the addition of counterterms to the Lagrangian, giving the first complete proof of the cancellation of all divergences in an arbitrary interaction. The author also introduces a new method of renormalizing an arbitrary Feynman amplitude, a method that is simpler than previous approaches and can be used to study the renormalized perturbation series in quantum field theory.
Present State Of Rigorous Analytic Properties Of Scattering Amplitudes
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Author : Gustav Sommer
language : en
Publisher:
Release Date : 1970
Present State Of Rigorous Analytic Properties Of Scattering Amplitudes written by Gustav Sommer and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1970 with categories.
A Study Of Analytic Properties Of Scattering Amplitudes
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Author : J. Chela-Flores
language : en
Publisher:
Release Date : 1967
A Study Of Analytic Properties Of Scattering Amplitudes written by J. Chela-Flores and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1967 with S-matrix theory categories.
Analytic Tools For Feynman Integrals
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Author : Vladimir A. Smirnov
language : en
Publisher: Springer
Release Date : 2013-01-16
Analytic Tools For Feynman Integrals written by Vladimir A. Smirnov and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-01-16 with Science categories.
The goal of this book is to describe the most powerful methods for evaluating multiloop Feynman integrals that are currently used in practice. This book supersedes the author’s previous Springer book “Evaluating Feynman Integrals” and its textbook version “Feynman Integral Calculus.” Since the publication of these two books, powerful new methods have arisen and conventional methods have been improved on in essential ways. A further qualitative change is the fact that most of the methods and the corresponding algorithms have now been implemented in computer codes which are often public. In comparison to the two previous books, three new chapters have been added: One is on sector decomposition, while the second describes a new method by Lee. The third new chapter concerns the asymptotic expansions of Feynman integrals in momenta and masses, which were described in detail in another Springer book, “Applied Asymptotic Expansions in Momenta and Masses,” by the author. This chapter describes, on the basis of papers that appeared after the publication of said book, how to algorithmically discover the regions relevant to a given limit within the strategy of expansion by regions. In addition, the chapters on the method of Mellin-Barnes representation and on the method of integration by parts have been substantially rewritten, with an emphasis on the corresponding algorithms and computer codes.