Combinatorial Aspects Of Scattering Amplitudes
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Combinatorial Aspects Of Scattering Amplitudes
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Author : Matteo Parisi
language : en
Publisher: Springer Nature
Release Date : 2023-12-11
Combinatorial Aspects Of Scattering Amplitudes written by Matteo Parisi and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-12-11 with Science categories.
This book is a significant contribution within and across High Energy Physics and Algebraic Combinatorics. It is at the forefront of the recent paradigm shift according to which physical observables emerge from geometry and combinatorics. It is the first book on the amplituhedron, which encodes the scattering amplitudes of N=4 Yang-Mills theory, a cousin of the theory of strong interactions of quarks and gluons. Amplituhedra are generalizations of polytopes inside the Grassmannian, and they build on the theory of total positivity and oriented matroids. This book unveils many new combinatorial structures of the amplituhedron and introduces a new important related object, the momentum amplituhedron. Moreover, the work pioneers the connection between amplituhedra, cluster algebras and tropical geometry. Combining extensive introductions with proofs and examples, it is a valuable resource for researchers investigating geometrical structures emerging from physics for some time to come.
Aspects Of Scattering Amplitudes And Moduli Space Localization
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Author : Sebastian Mizera
language : en
Publisher: Springer Nature
Release Date : 2020-09-23
Aspects Of Scattering Amplitudes And Moduli Space Localization written by Sebastian Mizera and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-09-23 with Science categories.
This thesis proposes a new perspective on scattering amplitudes in quantum field theories. Their standard formulation in terms of sums over Feynman diagrams is replaced by a computation of geometric invariants, called intersection numbers, on moduli spaces of Riemann surfaces. It therefore gives a physical interpretation of intersection numbers, which have been extensively studied in the mathematics literature in the context of generalized hypergeometric functions. This book explores physical consequences of this formulation, such as recursion relations, connections to geometry and string theory, as well as a phenomenon called moduli space localization. After reviewing necessary mathematical background, including topology of moduli spaces of Riemann spheres with punctures and its fundamental group, the definition and properties of intersection numbers are presented. A comprehensive list of applications and relations to other objects is given, including those to scattering amplitudes in open- and closed-string theories. The highlights of the thesis are the results regarding localization properties of intersection numbers in two opposite limits: in the low- and the high-energy expansion. In order to facilitate efficient computations of intersection numbers the author introduces recursion relations that exploit fibration properties of the moduli space. These are formulated in terms of so-called braid matrices that encode the information of how points braid around each other on the corresponding Riemann surface. Numerous application of this approach are presented for computation of scattering amplitudes in various gauge and gravity theories. This book comes with an extensive appendix that gives a pedagogical introduction to the topic of homologies with coefficients in a local system.
Grassmannian Geometry Of Scattering Amplitudes
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Author : Nima Arkani-Hamed
language : en
Publisher: Cambridge University Press
Release Date : 2016-05-05
Grassmannian Geometry Of Scattering Amplitudes written by Nima Arkani-Hamed and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-05-05 with Mathematics categories.
An essential guide to peturbative quantum field theory and its connection to Grassmannian geometry.
Grassmannian Geometry Of Scattering Amplitudes
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Author :
language : en
Publisher:
Release Date : 2016
Grassmannian Geometry Of Scattering Amplitudes written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016 with Combinatorial analysis categories.
Scattering Amplitudes And Wilson Loops In Twistor Space
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Author : Mathew Richard Bullimore
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-10-22
Scattering Amplitudes And Wilson Loops In Twistor Space written by Mathew Richard Bullimore and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-10-22 with Science categories.
Scattering amplitudes are fundamental and rich observables in quantum field theory. Based on the observation that, for massless particles of spin-one or more, scattering amplitudes are much simpler than expected from traditional Feynman diagram techniques, the broad aim of this work is to understand and exploit this hidden structure. It uses methods from twistor theory to provide new insights into the correspondence between scattering amplitudes in supersymmetric Yang-Mills theory and null polygonal Wilson loops. By additionally exploiting the symmetries of the problem, the author succeeds in developing new ways of computing scattering amplitudes.
Scattering Amplitudes In Gauge Theories
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Author : Johannes M. Henn
language : en
Publisher: Springer
Release Date : 2014-02-07
Scattering Amplitudes In Gauge Theories written by Johannes M. Henn and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-02-07 with Science categories.
At the fundamental level, the interactions of elementary particles are described by quantum gauge field theory. The quantitative implications of these interactions are captured by scattering amplitudes, traditionally computed using Feynman diagrams. In the past decade tremendous progress has been made in our understanding of and computational abilities with regard to scattering amplitudes in gauge theories, going beyond the traditional textbook approach. These advances build upon on-shell methods that focus on the analytic structure of the amplitudes, as well as on their recently discovered hidden symmetries. In fact, when expressed in suitable variables the amplitudes are much simpler than anticipated and hidden patterns emerge. These modern methods are of increasing importance in phenomenological applications arising from the need for high-precision predictions for the experiments carried out at the Large Hadron Collider, as well as in foundational mathematical physics studies on the S-matrix in quantum field theory. Bridging the gap between introductory courses on quantum field theory and state-of-the-art research, these concise yet self-contained and course-tested lecture notes are well-suited for a one-semester graduate level course or as a self-study guide for anyone interested in fundamental aspects of quantum field theory and its applications. The numerous exercises and solutions included will help readers to embrace and apply the material present ed in the main text.
Modern Analytic Methods For Computing Scattering Amplitudes
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Author : Simone Zoia
language : en
Publisher:
Release Date : 2022
Modern Analytic Methods For Computing Scattering Amplitudes written by Simone Zoia and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022 with 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.sses of phenomenological interest, such as three-photon, three-jet, and di-photon + jet production.
Recent Trends In Algebraic Combinatorics
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Author : Hélène Barcelo
language : en
Publisher: Springer
Release Date : 2019-01-21
Recent Trends In Algebraic Combinatorics written by Hélène Barcelo and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-01-21 with Mathematics categories.
This edited volume features a curated selection of research in algebraic combinatorics that explores the boundaries of current knowledge in the field. Focusing on topics experiencing broad interest and rapid growth, invited contributors offer survey articles on representation theory, symmetric functions, invariant theory, and the combinatorics of Young tableaux. The volume also addresses subjects at the intersection of algebra, combinatorics, and geometry, including the study of polytopes, lattice points, hyperplane arrangements, crystal graphs, and Grassmannians. All surveys are written at an introductory level that emphasizes recent developments and open problems. An interactive tutorial on Schubert Calculus emphasizes the geometric and topological aspects of the topic and is suitable for combinatorialists as well as geometrically minded researchers seeking to gain familiarity with relevant combinatorial tools. Featured authors include prominent women in the field known for their exceptional writing of deep mathematics in an accessible manner. Each article in this volume was reviewed independently by two referees. The volume is suitable for graduate students and researchers interested in algebraic combinatorics.
Essentials Of Tropical Combinatorics
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Author : Michael Joswig
language : en
Publisher: American Mathematical Society
Release Date : 2021-12-08
Essentials Of Tropical Combinatorics written by Michael Joswig and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-12-08 with Mathematics categories.
The goal of this book is to explain, at the graduate student level, connections between tropical geometry and optimization. Building bridges between these two subject areas is fruitful in two ways. Through tropical geometry optimization algorithms become applicable to questions in algebraic geometry. Conversely, looking at topics in optimization through the tropical geometry lens adds an additional layer of structure. The author covers contemporary research topics that are relevant for applications such as phylogenetics, neural networks, combinatorial auctions, game theory, and computational complexity. This self-contained book grew out of several courses given at Technische Universität Berlin and elsewhere, and the main prerequisite for the reader is a basic knowledge in polytope theory. It contains a good number of exercises, many examples, beautiful figures, as well as explicit tools for computations using $texttt{polymake}$.
Limits Of Graphs In Group Theory And Computer Science
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Author : Goulnara Arzhantseva
language : en
Publisher: EPFL Press
Release Date : 2009-03-16
Limits Of Graphs In Group Theory And Computer Science written by Goulnara Arzhantseva and has been published by EPFL Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-03-16 with Mathematics categories.
A collection of research articles and survey papers, this text highlights current methods and open problems in the geometric, combinatorial, and computational aspects of group theory. New interactions with broad areas of theoretical computer science are also considered. Pub 3/09.