Modern Analytic Methods For Computing Scattering Amplitudes

Author : Simone Zoia
Publisher : Springer Nature
Page : 221 pages
File Size : 44,5 Mb
Release : 2022-05-18
Category : Science
ISBN : 9783031019456

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Modern Analytic Methods for Computing Scattering Amplitudes by Simone Zoia Pdf

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.

Author : Johannes M. Henn,Jan C. Plefka
Publisher : Springer
Page : 206 pages
File Size : 50,5 Mb
Release : 2014-02-07
Category : Science
ISBN : 9783642540226

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Scattering Amplitudes in Gauge Theories by Johannes M. Henn,Jan C. Plefka Pdf

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.

Author : André Martin (Professeur.),Franklin Cheung
Publisher : M.E. Sharpe
Page : 152 pages
File Size : 52,7 Mb
Release : 1970
Category : Science
ISBN : UCAL:$B77320

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Analyticity Properties and Bounds of the Scattering Amplitudes by André Martin (Professeur.),Franklin Cheung Pdf

Author : Mathew Richard Bullimore
Publisher : Springer Science & Business Media
Page : 118 pages
File Size : 48,9 Mb
Release : 2013-10-22
Category : Science
ISBN : 9783319009094

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Scattering Amplitudes and Wilson Loops in Twistor Space by Mathew Richard Bullimore Pdf

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.

Author : Herch Moyses Nussenzveig
Publisher : Unknown
Page : 170 pages
File Size : 46,6 Mb
Release : 1962
Category : Particles (Nuclear physics)
ISBN : UOM:39015017251631

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Analytic Properties of Non-relativistic Scattering Amplitudes by Herch Moyses Nussenzveig Pdf

Author : Jochen Brüning,Matthias Staudacher
Publisher : Walter de Gruyter GmbH & Co KG
Page : 517 pages
File Size : 49,7 Mb
Release : 2018-04-09
Category : Mathematics
ISBN : 9783110451535

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Space – Time – Matter by Jochen Brüning,Matthias Staudacher Pdf

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

Author : Alexander G. Ramm
Publisher : Springer Science & Business Media
Page : 131 pages
File Size : 47,8 Mb
Release : 2012-12-06
Category : Science
ISBN : 9781461257158

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Iterative Methods for Calculating Static Fields and Wave Scattering by Small Bodies by Alexander G. Ramm Pdf

Iterative methods for calculating static fields are presented in this book. Static field boundary value problems are reduced to the boundary integral equations and these equations are solved by means of iterative processes. This is done for interior and exterior problems and for var ious boundary conditions. Most problems treated are three-dimensional, because for two-dimensional problems the specific and often powerful tool of conformal mapping is available. The iterative methods have some ad vantages over grid methods and, to a certain extent, variational methods: (1) they give analytic approximate formulas for the field and for some functionals of the field of practical importance (such as capacitance and polarizability tensor), (2) the formulas for the functionals can be used in a computer program for calculating these functionals for bodies of arbitrary shape, (3) iterative methods are convenient for computers. From a practical point of view the above methods reduce to the cal culation of multiple integrals. Of special interest is the case of inte grands with weak singularities. Some of the central results of the book are some analytic approximate formulas for scattering matrices for small bodies of arbitrary shape. These formulas answer many practical questions such as how does the scattering depend on the shape of the body or on the boundary conditions, how does one calculate the effective field in a medium consisting of many small particles, and many other questions.

Author : Henriette Elvang,Yu-tin Huang
Publisher : Cambridge University Press
Page : 337 pages
File Size : 49,5 Mb
Release : 2015-02-05
Category : Science
ISBN : 9781107069251

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Scattering Amplitudes in Gauge Theory and Gravity by Henriette Elvang,Yu-tin Huang Pdf

This book provides a comprehensive, pedagogical introduction to scattering amplitudes in gauge theory and gravity for graduate students.

Author : Simon Badger,Johannes Henn,Jan Christoph Plefka,Simone Zoia
Publisher : Springer Nature
Page : 312 pages
File Size : 50,5 Mb
Release : 2024-02-01
Category : Science
ISBN : 9783031469879

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Scattering Amplitudes in Quantum Field Theory by Simon Badger,Johannes Henn,Jan Christoph Plefka,Simone Zoia Pdf

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.

Author : Alekseĭ Grigorʹevich Sitenko
Publisher : Springer
Page : 316 pages
File Size : 46,8 Mb
Release : 1991-01-21
Category : Computers
ISBN : UCSD:31822006405609

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Scattering Theory by Alekseĭ Grigorʹevich Sitenko Pdf

This book is based on the course in theoretical nuclear physics that has been given by the author for some years at the T. G. Shevchenko Kiev State University. This version is supplemented and revised to include new results obtained after 1971 and 1975 when the first and second editions were published. This text is intended as an introduction to the nonrelativistic theory of po tential scattering. The analysis is based on the scattering matrix concept where the relationship between the scattering matrix and observable physical quantities is considered. The stationary formulation of the scattering problem is presented; particle wave functions in the external field are obtained. A formulation of the optical theorem is given as well as a discussion on time inversion and the reci procity theorem. Analytic properties of the scattering matrix, dispersion relations, and complex moments are analyzed. The dispersion relations for an arbitrary di rection scattering amplitude are proven, and analytic properties of the amplitude in the plane of the complex cosine of the scattering angle are studied in detail.

Author : Fadil Santosa,Ivar Stakgold
Publisher : CRC Press
Page : 292 pages
File Size : 45,9 Mb
Release : 2019-05-07
Category : Mathematics
ISBN : 9780429525087

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Analytical and Computational Methods in Scattering and Applied Mathematics by Fadil Santosa,Ivar Stakgold Pdf

Professor Ralph Kleinman was director of the Center for the Mathematics of Waves and held the UNIDEL Professorship of the University of Delaware. Before his death in 1998, he made major scientific contributions in the areas of electromagnetic scattering, wave propagation, and inverse problems. He was instrumental in bringing together the mathematic

Author : Asim Orhan Barut
Publisher : Unknown
Page : 448 pages
File Size : 50,8 Mb
Release : 1969
Category : Science
ISBN : UCAL:B3375487

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Scattering Theory by Asim Orhan Barut Pdf

Author : Alekseĭ Grigorʹevich Sitenko
Publisher : Pergamon
Page : 288 pages
File Size : 48,7 Mb
Release : 1971
Category : Scattering (Physics).
ISBN : UCAL:B4282970

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Lectures in Scattering Theory by Alekseĭ Grigorʹevich Sitenko Pdf

Author : Aleksei G. Sitenko
Publisher : Springer
Page : 0 pages
File Size : 49,9 Mb
Release : 1991
Category : Science
ISBN : 3642840345

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Scattering Theory by Aleksei G. Sitenko Pdf

This book is based on the course in theoretical nuclear physics that has been given by the author for some years at the T. G. Shevchenko Kiev State University. This version is supplemented and revised to include new results obtained after 1971 and 1975 when the first and second editions were published. This text is intended as an introduction to the nonrelativistic theory of po tential scattering. The analysis is based on the scattering matrix concept where the relationship between the scattering matrix and observable physical quantities is considered. The stationary formulation of the scattering problem is presented; particle wave functions in the external field are obtained. A formulation of the optical theorem is given as well as a discussion on time inversion and the reci procity theorem. Analytic properties of the scattering matrix, dispersion relations, and complex moments are analyzed. The dispersion relations for an arbitrary di rection scattering amplitude are proven, and analytic properties of the amplitude in the plane of the complex cosine of the scattering angle are studied in detail.

Author : Kurt H Becker
Publisher : World Scientific
Page : 356 pages
File Size : 52,9 Mb
Release : 1998-05-21
Category : Electronic
ISBN : 9789814496179

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Novel Aspects of Electron-Molecule Collisions by Kurt H Becker Pdf

Electron–molecule collisions have been studied extensively by both experimentalists and theorists since the early years of this century. The past ten years have seen a remarkable renaissance in experimental and theoretical activities in the study of electron collision processes with molecules. This was stimulated (i) by the advent of more powerful computers and new theoretical concepts that allow the study of complex targets and collision processes with a multitude of final states (such as ionization and dissociation) and the investigation of collisions with oriented and aligned molecules, (ii) by advances in experimental instrumentation (improved electron spectrometers, intense sources of spin-polarized electrons, position-sensitive detectors), and (iii) by the discovery of a new class of species, e.g. large stable carbon clusters or “fullerenes”, which opened up a new field of theoretical and experimental research in which collisions involving fullerenes as targets or as projectiles constitute an important component. Lastly, electron–molecule collisions are a key component in efforts to characterize, diagnose, describe and model the complex processes in low-temperature plasmas, which are of ever-increasing importance in many rapidly developing high-tech applications (such as the fabrication of microelectronic chips), in the controlled deposition of thin films and in plasma-assisted surface-modification processes. This book covers the activities in all those areas. Contents:Positive and Negative Ion Formation in Electron Collisions with Fullerenes (S Matt et al.)The Scattering of Low-Energy Electrons and Positrons from Polar Targets: Experimental and Theoretical Difficulties (F A Gianturco & P Paioletti)Spin Effects in Electron Molecule Collisions (G F Hanne)Collisions with Oriented and Aligned Molecules (A Busalla & K Blum)Recent Developments in Electron Momentum Density Measurements of Polyatomics by Molecular (e,2e) Spectroscopy (K T Leung)Electron Impact Dissociative Excitation and Ionization of Molecular Ions (G H Dunn & N Djuric)Electron-Molecule Cross Sections for Plasma Applications: The Role of Internal Energy of the Target (M Capitelli & R Celiberto)Improvements to the “Standard” Complex Kohn Variational Method: Towards the Development of an “R-Matrix Theory without a Box” (T N Rescigno & C W McCurdy) Readership: Students and researchers in atomic and molecular physics. Keywords: