The Analytic S Matrix

Author : R. J. Eden
Publisher : Cambridge University Press
ISBN 13 : 9780521523363
Total Pages : 300 pages
Book Rating : 4.62/5 ( download)

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Download or read book The Analytic S-Matrix written by R. J. Eden and published by Cambridge University Press. This book was released on 2002-04-30 with total page 300 pages. Available in PDF, EPUB and Kindle. Book excerpt: A theory of the S-Matrix, starting from physically plausible assumptions and looking at the mathematical consequences.

Author : Richard John Eden
Publisher :
ISBN 13 :
Total Pages : 287 pages
Book Rating : 4.72/5 ( download)

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Download or read book The Analytic S-Matrix, By R.J. Eden And Others written by Richard John Eden and published by . This book was released on 1966 with total page 287 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Author : Richard John Eden
Publisher :
ISBN 13 :
Total Pages : 287 pages
Book Rating : 4.01/5 ( download)

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Download or read book The Analytic S-matrix, by R.J. Eden [and Others]. written by Richard John Eden and published by . This book was released on 1966 with total page 287 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Author : Geoffrey F. Chew
Publisher :
ISBN 13 :
Total Pages : 136 pages
Book Rating : 4.04/5 ( download)

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Download or read book The Analytic S Matrix written by Geoffrey F. Chew and published by . This book was released on 1966 with total page 136 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Author : G. Latouche
Publisher : SIAM
ISBN 13 : 0898714257
Total Pages : 331 pages
Book Rating : 4.58/5 ( download)

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Download or read book Introduction to Matrix Analytic Methods in Stochastic Modeling written by G. Latouche and published by SIAM. This book was released on 1999-01-01 with total page 331 pages. Available in PDF, EPUB and Kindle. Book excerpt: Presents the basic mathematical ideas and algorithms of the matrix analytic theory in a readable, up-to-date, and comprehensive manner.

Author : W.F.Jr. Donoghue
Publisher : Springer Science & Business Media
ISBN 13 : 3642657559
Total Pages : 191 pages
Book Rating : 4.59/5 ( download)

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Download or read book Monotone Matrix Functions and Analytic Continuation written by W.F.Jr. Donoghue and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 191 pages. Available in PDF, EPUB and Kindle. Book excerpt: A Pick function is a function that is analytic in the upper half-plane with positive imaginary part. In the first part of this book we try to give a readable account of this class of functions as well as one of the standard proofs of the spectral theorem based on properties of this class. In the remainder of the book we treat a closely related topic: Loewner's theory of monotone matrix functions and his analytic continuation theorem which guarantees that a real function on an interval of the real axis which is a monotone matrix function of arbitrarily high order is the restriction to that interval of a Pick function. In recent years this theorem has been complemented by the Loewner-FitzGerald theorem, giving necessary and sufficient conditions that the continuation provided by Loewner's theorem be univalent. In order that our presentation should be as complete and trans parent as possible, we have adjoined short chapters containing the in formation about reproducing kernels, almost positive matrices and certain classes of conformal mappings needed for our proofs.

Author : Holmfridur Sigridar Hannesdottir
Publisher : Springer Nature
ISBN 13 : 3031182588
Total Pages : 165 pages
Book Rating : 4.87/5 ( download)

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Download or read book What is the iε for the S-matrix? written by Holmfridur Sigridar Hannesdottir and published by Springer Nature. This book was released on 2023-01-01 with total page 165 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a modern perspective on the analytic structure of scattering amplitudes in quantum field theory, with the goal of understanding and exploiting consequences of unitarity, causality, and locality. It focuses on the question: Can the S-matrix be complexified in a way consistent with causality? The affirmative answer has been well understood since the 1960s, in the case of 2→2 scattering of the lightest particle in theories with a mass gap at low momentum transfer, where the S-matrix is analytic everywhere except at normal-threshold branch cuts. We ask whether an analogous picture extends to realistic theories, such as the Standard Model, that include massless fields, UV/IR divergences, and unstable particles. Especially in the presence of light states running in the loops, the traditional iε prescription for approaching physical regions might break down, because causality requirements for the individual Feynman diagrams can be mutually incompatible. We demonstrate that such analyticity problems are not in contradiction with unitarity. Instead, they should be thought of as finite-width effects that disappear in the idealized 2→2 scattering amplitudes with no unstable particles, but might persist at higher multiplicity. To fix these issues, we propose an iε-like prescription for deforming branch cuts in the space of Mandelstam invariants without modifying the analytic properties of the physical amplitude. This procedure results in a complex strip around the real part of the kinematic space, where the S-matrix remains causal. We illustrate all the points on explicit examples, both symbolically and numerically, in addition to giving a pedagogical introduction to the analytic properties of the perturbative S-matrix from a modern point of view. To help with the investigation of related questions, we introduce a number of tools, including holomorphic cutting rules, new approaches to dispersion relations, as well as formulae for local behavior of Feynman integrals near branch points. This book is well suited for anyone with knowledge of quantum field theory at a graduate level who wants to become familiar with the complex-analytic structure of Feynman integrals.

Author : Elizabeth A. Rauscher
Publisher : World Scientific
ISBN 13 : 9814324248
Total Pages : 412 pages
Book Rating : 4.43/5 ( download)

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Download or read book Orbiting the Moons of Pluto written by Elizabeth A. Rauscher and published by World Scientific. This book was released on 2011 with total page 412 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Maxwell, Einstein, Schr”dinger and Dirac equations are considered the most important equations in all of physics. This volume aims to provide new eight- and twelve-dimensional complex solutions to these equations for the first time in order to reveal their richness and continued importance for advancing fundamental Physics. If M-Theory is to keep its promise of defining the ultimate structure of matter and spacetime, it is only through the topological configurations of additional dimensionality (or degrees of freedom) that this will be possible. Stretching the exploration of complex space through all of the main equations of Physics should help tighten the noose on ?the? fundamental theory. This kind of exploration of higher dimensional spacetime has for the most part been neglected by M-theorists and physicists in general and is taken to its penultimate form here.

Author : Simone Zoia
Publisher : Springer Nature
ISBN 13 : 3031019458
Total Pages : 221 pages
Book Rating : 4.56/5 ( download)

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Download or read book Modern Analytic Methods for Computing Scattering Amplitudes written by Simone Zoia and published by Springer Nature. This book was released on 2022-05-18 with total page 221 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : S. Chakravarthy
Publisher : CRC Press
ISBN 13 : 9780824797669
Total Pages : 400 pages
Book Rating : 4.63/5 ( download)

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Download or read book Matrix-Analytic Methods in Stochastic Models written by S. Chakravarthy and published by CRC Press. This book was released on 1996-09-19 with total page 400 pages. Available in PDF, EPUB and Kindle. Book excerpt: Based on the proceedings of the first International Conference on Matrix-Analytic Methods (MAM) in Stochastic Models, held in Flint, Michigan, this book presents a general working knowledge of MAM through tutorial articles and application papers. It furnishes information on MAM studies carried out in the former Soviet Union.