Grassmannian Geometry Of Scattering Amplitudes

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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 In Quantum Field Theory

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Author : Simon Badger
language : en
Publisher: Springer Nature
Release Date : 2023-12-31

Scattering Amplitudes In Quantum Field Theory written by Simon Badger and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-12-31 with Science categories.

This open access book bridges a gap between introductory Quantum Field Theory (QFT) courses and state-of-the-art research in scattering amplitudes. It covers the path from basic definitions of QFT to amplitudes, which are relevant for processes in the Standard Model of particle physics. The book begins with a concise yet self-contained introduction to QFT, including perturbative quantum gravity. It then presents modern methods for calculating scattering amplitudes, focusing on tree-level amplitudes, loop-level integrands and loop integration techniques. These methods help to reveal intriguing relations between gauge and gravity amplitudes and are of increasing importance for obtaining high-precision predictions for collider experiments, such as those at the Large Hadron Collider, as well as for foundational mathematical physics studies in QFT, including recent applications to gravitational wave physics.These course-tested lecture notes include numerous exercises with solutions. Requiring only minimal knowledge of QFT, they are well-suited for MSc and PhD students as a preparation for research projects in theoretical particle physics. They can be used as a one-semester graduate level course, or as a self-study guide for researchers interested in fundamental aspects of quantum field theory.

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.

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.

Combinatorial Aspects Of Scattering Amplitudes

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Author : Matteo Parisi
language : en
Publisher: Springer Nature
Release Date : 2023-11-09

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 2023-11-09 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.

Anticipating The Next Discoveries In Particle Physics Tasi 2016 Proceedings Of The 2016 Theoretical Advanced Study Institute In Elementary Particle Physics

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Author : Rouven Essig
language : en
Publisher: World Scientific
Release Date : 2018-05-22

Anticipating The Next Discoveries In Particle Physics Tasi 2016 Proceedings Of The 2016 Theoretical Advanced Study Institute In Elementary Particle Physics written by Rouven Essig and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-05-22 with Science categories.

This volume is a compilation of lectures delivered at the TASI 2016 summer school, 'Anticipating the Next Discoveries in Particle Physics', held at the University of Colorado at Boulder in June 2016. The school focused on topics in theoretical particle physics, phenomenology, dark matter, and cosmology of interest to contemporary researchers in these fields. The lectures are accessible to graduate students in the initial stages of their research careers.

Conversations On Quantum Gravity

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Author : Jácome Armas
language : en
Publisher: Cambridge University Press
Release Date : 2021-08-26

Conversations On Quantum Gravity written by Jácome Armas 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 2021-08-26 with Biography & Autobiography categories.

Leading theorists share their important insights into the ongoing quest of theoretical physics to find a quantum theory of gravity.

Topological Geometrodynamics

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Author : Matti Pitkanen
language : en
Publisher: Luniver Press
Release Date : 2006

Topological Geometrodynamics written by Matti Pitkanen and has been published by Luniver Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006 with Mathematics categories.

Topological GeometroDynamics is a modification of general relativity inspired by the conceptual problems related to the definitions of inertial and gravitational energy in general relativity. Topological geometrodynamics can be also seen as a generalization of super string models. Physical space-times are seen as four-dimensional surfaces in certain eight-dimensional space. The choice of this space is fixed by symmetries of the standard model so that geometrization of known classical fields and elementary particle quantum numbers results. The notion of many-sheeted space-time allows re-interpretation of the structures of perceived world in terms of macroscopic space-time topology. The generalization of the number concept based on fusion of real numbers and p-adic number fields implies a further generalization of the space-time concept allowing to identify space-time correlates of cognition and intentionality. Quantum measurement theory extended to a quantum theory of consciousness becomes an organic part of theory. A highly non-trivial prediction is the existence of a fractal hierarchy of copies of standard model physics with dark matter identified in terms of macroscopic quantum phases characterized by dynamical and quantized Planck constant. The book is a comprehensive overview and analysis of topological geometrodynamics as a mathematical and physical theory.

Space Time Matter

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Author : Jochen Brüning
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2018-04-09

Space Time Matter written by Jochen Brüning and has been published by Walter de Gruyter GmbH & Co KG this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-04-09 with Mathematics categories.

This monograph describes some of the most interesting results obtained by the mathematicians and physicists collaborating in the CRC 647 "Space – Time – Matter", in the years 2005 - 2016. The work presented concerns the mathematical and physical foundations of string and quantum field theory as well as cosmology. Important topics are the spaces and metrics modelling the geometry of matter, and the evolution of these geometries. The partial differential equations governing such structures and their singularities, special solutions and stability properties are discussed in detail. Contents Introduction Algebraic K-theory, assembly maps, controlled algebra, and trace methods Lorentzian manifolds with special holonomy – Constructions and global properties Contributions to the spectral geometry of locally homogeneous spaces On conformally covariant differential operators and spectral theory of the holographic Laplacian Moduli and deformations Vector bundles in algebraic geometry and mathematical physics Dyson–Schwinger equations: Fix-point equations for quantum fields Hidden structure in the form factors ofN = 4 SYM On regulating the AdS superstring Constraints on CFT observables from the bootstrap program Simplifying amplitudes in Maxwell-Einstein and Yang-Mills-Einstein supergravities Yangian symmetry in maximally supersymmetric Yang-Mills theory Wave and Dirac equations on manifolds Geometric analysis on singular spaces Singularities and long-time behavior in nonlinear evolution equations and general relativity