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Combinatorial Aspects Of Scattering Amplitudes
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Book Synopsis Combinatorial Aspects of Scattering Amplitudes by : Matteo Parisi
Download or read book Combinatorial Aspects of Scattering Amplitudes written by Matteo Parisi and published by Springer Nature. This book was released on 2023-12-11 with total page 237 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Aspects of Scattering Amplitudes and Moduli Space Localization by : Sebastian Mizera
Download or read book Aspects of Scattering Amplitudes and Moduli Space Localization written by Sebastian Mizera and published by Springer Nature. This book was released on 2020-09-23 with total page 148 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Grassmannian Geometry of Scattering Amplitudes by : Nima Arkani-Hamed
Download or read book Grassmannian Geometry of Scattering Amplitudes written by Nima Arkani-Hamed and published by Cambridge University Press. This book was released on 2016-05-05 with total page 205 pages. Available in PDF, EPUB and Kindle. Book excerpt: An essential guide to peturbative quantum field theory and its connection to Grassmannian geometry.
Book Synopsis Grassmannian Geometry of Scattering Amplitudes by :
Download or read book Grassmannian Geometry of Scattering Amplitudes written by and published by . This book was released on 2016 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Grassmannian Geometry of Scattering Amplitudes by : Nima Arkani-Hamed
Download or read book Grassmannian Geometry of Scattering Amplitudes written by Nima Arkani-Hamed and published by Cambridge University Press. This book was released on 2016-05-05 with total page 205 pages. Available in PDF, EPUB and Kindle. Book excerpt: Outlining a revolutionary reformulation of the foundations of perturbative quantum field theory, this book is a self-contained and authoritative analysis of the application of this new formulation to the case of planar, maximally supersymmetric Yang–Mills theory. The book begins by deriving connections between scattering amplitudes and Grassmannian geometry from first principles before introducing novel physical and mathematical ideas in a systematic manner accessible to both physicists and mathematicians. The principle players in this process are on-shell functions which are closely related to certain sub-strata of Grassmannian manifolds called positroids - in terms of which the classification of on-shell functions and their relations becomes combinatorially manifest. This is an essential introduction to the geometry and combinatorics of the positroid stratification of the Grassmannian and an ideal text for advanced students and researchers working in the areas of field theory, high energy physics, and the broader fields of mathematical physics.
Author :Mathew Richard Bullimore Publisher :Springer Science & Business Media ISBN 13 :3319009095 Total Pages :118 pages Book Rating :4.3/5 (19 download)
Book Synopsis Scattering Amplitudes and Wilson Loops in Twistor Space by : Mathew Richard Bullimore
Download or read book Scattering Amplitudes and Wilson Loops in Twistor Space written by Mathew Richard Bullimore and published by Springer Science & Business Media. This book was released on 2013-10-22 with total page 118 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Scattering Amplitudes in Gauge Theories by : Johannes M. Henn
Download or read book Scattering Amplitudes in Gauge Theories written by Johannes M. Henn and published by Springer. This book was released on 2014-02-07 with total page 206 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Recent Trends in Algebraic Combinatorics by : Hélène Barcelo
Download or read book Recent Trends in Algebraic Combinatorics written by Hélène Barcelo and published by Springer. This book was released on 2019-01-21 with total page 362 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Essentials of Tropical Combinatorics by : Michael Joswig
Download or read book Essentials of Tropical Combinatorics written by Michael Joswig and published by American Mathematical Society. This book was released on 2021-12-08 with total page 398 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 $texttt{polymake}$.
Download or read book Nuclear Science Abstracts written by and published by . This book was released on 1974 with total page 764 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Limits of Graphs in Group Theory and Computer Science by : Goulnara Arzhantseva
Download or read book Limits of Graphs in Group Theory and Computer Science written by Goulnara Arzhantseva and published by EPFL Press. This book was released on 2009-03-16 with total page 312 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Combinatorial Aspect of Integrable Systems by : Arkady Berenstein
Download or read book Combinatorial Aspect of Integrable Systems written by Arkady Berenstein and published by . This book was released on 2007 with total page 184 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is a collection of six papers based on the expository lectures of the workshop "Combinatorial Aspect of Integrable Systems" held at RIMS during July 26-30, 2004, as a part of the Project Research 2004 "Method of Algebraic Analysis in Integrable Systems". The topics range over crystal bases of quantum groups, its algebra-geometric analogue known as geometric crystal, generalizations of Robinson-Schensted type correspondence, fermionic formula related to Bethe ansatz, applications of crystal bases to soliton celluar automata, Yang-Baxter maps, and integrable discrete dynamics. All the papers are friendly written with many illustrative examples and intimately related to each other. This volume will serve as a good guide for researchers and graduate students who are interested in this fascinating subject.Published by Mathematical Society of Japan and distributed by World Scientific Publishing Co. for all markets
Book Synopsis A Combinatorial Perspective on Quantum Field Theory by : Karen Yeats
Download or read book A Combinatorial Perspective on Quantum Field Theory written by Karen Yeats and published by Springer. This book was released on 2016-11-23 with total page 120 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book explores combinatorial problems and insights in quantum field theory. It is not comprehensive, but rather takes a tour, shaped by the author’s biases, through some of the important ways that a combinatorial perspective can be brought to bear on quantum field theory. Among the outcomes are both physical insights and interesting mathematics. The book begins by thinking of perturbative expansions as kinds of generating functions and then introduces renormalization Hopf algebras. The remainder is broken into two parts. The first part looks at Dyson-Schwinger equations, stepping gradually from the purely combinatorial to the more physical. The second part looks at Feynman graphs and their periods. The flavour of the book will appeal to mathematicians with a combinatorics background as well as mathematical physicists and other mathematicians.
Book Synopsis At the Frontier of Particle Physics by : Mikhail A. Shifman
Download or read book At the Frontier of Particle Physics written by Mikhail A. Shifman and published by World Scientific. This book was released on 2001 with total page 708 pages. Available in PDF, EPUB and Kindle. Book excerpt: Introduction / M. Shifman -- Introducing Boris Ioffe / B.V. Geshkenbein -- Boris Lazarevich Ioffe is 75 / I.B. Khriplovich -- ch. 1. Pages of the past. A top secret assignment / B.L. Ioffe. Editor's comments. Snapshots from the 1950's / Yu. F. Orlov -- ch. 2. The making of QCD. Quantizing the Yang-Mills field / L.D. Faddeev. The discovery of asymptotic freedom and the emergence of QCD / D.J. Gross. Editor's note. Recollections on dimensional regularization and related topics / C.G. Bollini. Historical curiosity: how asymptotic freedom of the Yang-Mills theory could have been discovered three times before Gross, Wilczek, and politzer, but was not / M. Shifman -- ch. 3. From hadrons to nuclei: crossing the border / S.R. Beane [und weitere] -- ch. 4. Chiral dynamics / H. Leutwyler -- ch. 5. Aspects of chiral symmetry / A. Smilga -- ch. 6. Nucleons as chiral solitons / D. Diakonov and V. Yu. Petrov -- ch. 7. Chiral QCD: baryon dynamics / U. MeiBner -- ch. 8. Hadrons in the 1/N expansion / A.V. Manohar -- ch. 9. QCD inequalities / S. Nussinov -- ch. 10. Regge poles in QCD / A.B. Kaidalov -- ch. 11. Small x physics and the colored glass condensate / L. McLerran -- ch. 12. On Gribov's ideas on confinement / A. Vainshtein -- ch. 13. QCD in a finite volume / P. van Baal -- ch. 14. Compact variables and singular fields in QCD / F. Lenz and S. Wörlen -- ch. 15. Instanton-induced effects in QCD / E.V. Shuryak -- ch. 16. Perturbative QCD and the parton structure of the nucleon / W.-K. Tung -- ch. 17. Multiloop evolution of the QCD coupling constant and quark masses / K.G. Chetyrkin -- ch. 18. Multi-parton amplitudes in QCD / Z. Bern -- ch. 19. Generalized parton distributions / A. Radyushkin -- ch. 20. Analytical QCD and multiparticle production / V.A. Khoze, W. Ochs and J. Wosiek -- ch. 21. Space-time picture of high energy scattering / H.G. Dosch -- ch. 22. High-energy QCD and Wilson lines / I. Balitsky -- ch. 23. Exclusive processes in quantum chromodynamics and the light-cone Fock representation / S.J. Brodsky -- ch. 24. Quark-hadron duality / M. Shifman -- ch. 25. QCD sum rules, a modern perspective / P. Colangelo and A. Khodjamirian -- ch. 26. Topics in the heavy quark expansion / N. Uraltsev -- ch. 27. Weak decays of heavy quarks / F. De Fazio -- ch. 28. Renormalons and power corrections / M. Beneke and V.M. Braun -- ch. 29. Confinement, magnetic Z[symbol] symmetry and low-energy effective theory of gluodynamics / A. Kovner -- ch. 30. Flux tubes and confinement in the Seiberg-Witten theory: lessons for QCD / A. Yung -- ch. 31. Millennial messages for QCD from the superworld and from the string / M.J. Strassler -- ch. 32. The center symmetry and its spontaneous breakdown at high temperature / K. Holland and U.-J. Wiese -- ch. 33. 2D model field theories and finite temperature and density / V. Schön and M. Thies -- ch. 34. Hot and dense QCD / A.V. Smilga -- ch. 35. The condensed matter physics of QCD / K. Rajagopal and F. Wilczek
Book Synopsis At The Frontier Of Particle Physics: Handbook Of Qcd (In 3 Vols) by : Misha Shifman
Download or read book At The Frontier Of Particle Physics: Handbook Of Qcd (In 3 Vols) written by Misha Shifman and published by World Scientific. This book was released on 2001-04-10 with total page 2196 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book consists of reviews covering all aspects of quantum chromodynamics as we know it today. The articles have been written by recognized experts in this field, in honor of the 75th birthday of Professor Boris Ioffe. Combining features of a handbook and a textbook, this is the most comprehensive source of information on the present status of QCD. It is intended for students as well as physicists — both theorists and experimentalists.Each review is self-contained and pedagogically structured, providing the general formulation of the problem, telling where it stands with respect to other issues and why it is interesting and important, presenting the history of the subject, qualitative insights, and so on. The first part of the book is historical in nature. It includes, among other articles, Boris Ioffe's and Yuri Orlov's memoirs on high energy physics in the 1950's, a note by B V Geshkenbein on Ioffe's career in particle physics, and an essay on the discovery of asymptotic freedom written by David Gross.
Book Synopsis k-Schur Functions and Affine Schubert Calculus by : Thomas Lam
Download or read book k-Schur Functions and Affine Schubert Calculus written by Thomas Lam and published by Springer. This book was released on 2016-09-03 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book gives an introduction to the very active field of combinatorics of affine Schubert calculus, explains the current state of the art, and states the current open problems. Affine Schubert calculus lies at the crossroads of combinatorics, geometry, and representation theory. Its modern development is motivated by two seemingly unrelated directions. One is the introduction of k-Schur functions in the study of Macdonald polynomial positivity, a mostly combinatorial branch of symmetric function theory. The other direction is the study of the Schubert bases of the (co)homology of the affine Grassmannian, an algebro-topological formulation of a problem in enumerative geometry. This is the first introductory text on this subject. It contains many examples in Sage, a free open source general purpose mathematical software system, to entice the reader to investigate the open problems. This book is written for advanced undergraduate and graduate students, as well as researchers, who want to become familiar with this fascinating new field.
Book Synopsis Twistors in Mathematics and Physics by : T. N. Bailey
Download or read book Twistors in Mathematics and Physics written by T. N. Bailey and published by Cambridge University Press. This book was released on 1990-08-23 with total page 395 pages. Available in PDF, EPUB and Kindle. Book excerpt: This 1990 collection of review articles covers the considerable progress made in a wide range of applications of twistor theory.
