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Author: Matteo Parisi
Publisher: Springer Nature
ISBN: 3031410696
Category : Science
Languages : en
Pages : 237
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Book Description
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.
Author: Matteo Parisi
Publisher: Springer Nature
ISBN: 3031410696
Category : Science
Languages : en
Pages : 237
Get Book Here
Book Description
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.
Author: Nima Arkani-Hamed
Publisher: Cambridge University Press
ISBN: 1316571645
Category : Science
Languages : en
Pages : 205
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Book Description
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: Karen Yeats
Publisher: Springer
ISBN: 3319475517
Category : Science
Languages : en
Pages : 120
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Book Description
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.
Author: Nima Arkani-Hamed
Publisher: Cambridge University Press
ISBN: 1107086582
Category : Mathematics
Languages : en
Pages : 205
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Book Description
An essential guide to peturbative quantum field theory and its connection to Grassmannian geometry.
Author: Boyan Sirakov
Publisher: World Scientific
ISBN: 9813272899
Category : Mathematics
Languages : en
Pages : 5393
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Book Description
The Proceedings of the ICM publishes the talks, by invited speakers, at the conference organized by the International Mathematical Union every 4 years. It covers several areas of Mathematics and it includes the Fields Medal and Nevanlinna, Gauss and Leelavati Prizes and the Chern Medal laudatios.
Author: Mikhail A. Shifman
Publisher: World Scientific
ISBN: 9789810249670
Category : Medical
Languages : en
Pages : 708
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Book Description
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
Author: Misha Shifman
Publisher: World Scientific
ISBN: 9814492221
Category : Science
Languages : en
Pages : 2196
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Book Description
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.
Author: Sebastian Mizera
Publisher: Springer Nature
ISBN: 3030530108
Category : Science
Languages : en
Pages : 148
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Book Description
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.
Author: Arkady Berenstein
Publisher:
ISBN:
Category : Mathematics
Languages : en
Pages : 184
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Book Description
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
Author: T. N. Bailey
Publisher: Cambridge University Press
ISBN: 0521397839
Category : Mathematics
Languages : en
Pages : 395
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Book Description
This 1990 collection of review articles covers the considerable progress made in a wide range of applications of twistor theory.
