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Author : R. J. Eden,P. V. Landshoff,D. I. Olive,J. C. Polkinghorne
Publisher : Cambridge University Press
Page : 300 pages
File Size : 50,5 Mb
Release : 2002-04-30
Category : Mathematics
ISBN : 0521523362
A theory of the S-Matrix, starting from physically plausible assumptions and looking at the mathematical consequences.
Author : Richard John Eden
Publisher : Unknown
Page : 287 pages
File Size : 47,9 Mb
Release : 1966
Category : S-matrix theory
ISBN : OCLC:622871472
Author : Richard John Eden
Publisher : Unknown
Page : 287 pages
File Size : 54,8 Mb
Release : 1966
Category : S-matrix theory
ISBN : OCLC:639794001
Author : James T. Cushing
Publisher : Cambridge University Press
Page : 436 pages
File Size : 51,6 Mb
Release : 1990
Category : Mathematics
ISBN : 0521381819
Analyses what criteria should determine how scientific theories are selected and justified.
Author : Paul Urban
Publisher : Springer Science & Business Media
Page : 638 pages
File Size : 43,8 Mb
Release : 2012-12-06
Category : Science
ISBN : 9783709158357
We summarize the situation regarding non-polynomial Lagrangians: I should make the qualification that an enor mous amount of verification is needed before the problems of renormalizability are all sorted out, but one may ten tatively state: 1) All matrix elements are finite for theories where the Dyson index D is less than two. 2) For the cases when D=2 or 3, counter-terms have been explicitly written which absorb all infinities and the theories are renormalizable. 3) Mixed theories of polynomial and non-polynomial fields appear to be renormalizable provided the Dyson in dices separately and jointly fulfill renormalizability criteria. We believe that weak interactions, chiral La grangians and Yang-Mills theory fall into this class though detailed proofs have not yet been constructed. 4) It seems likely that to each order in the major coupling (and to all orders in the minor coupling}the S matrix elements, as computed by methods outlined, satisfy the necessary unitarity and analyticity requirements.
Author : Irinel Caprini
Publisher : Springer
Page : 130 pages
File Size : 43,7 Mb
Release : 2019-04-25
Category : Science
ISBN : 9783030189488
This book begins with a brief historical review of the early applications of standard dispersion relations in particle physics. It then presents the modern perspective within the Standard Model, emphasizing the relation of analyticity together with alternative tools applied to strong interactions, such as perturbative and lattice quantum chromodynamics (QCD), as well as chiral perturbation theory. The core of the book argues that, in order to improve the prediction of specific hadronic observables, it is often necessary to resort to methods of complex analysis more sophisticated than the simple Cauchy integral. Accordingly, a separate mathematical chapter is devoted to solving several functional analysis optimization problems. Their applications to physical amplitudes and form factors are discussed in the following chapters, which also demonstrate how to merge the analytic approach with statistical analysis tools. Given its scope, the book offers a valuable guide for researchers working in precision hadronic physics, as well as graduate students who are new to the field.
Author : T. W. Preist
Publisher : Springer
Page : 420 pages
File Size : 54,6 Mb
Release : 2014-11-14
Category : Science
ISBN : 9781489955296
Author : Berkovits Nathan Jacob,Brink Lars,Chau Ling-lie
Publisher : World Scientific
Page : 348 pages
File Size : 44,9 Mb
Release : 2017-06-20
Category : Science
ISBN : 9789813207868
Stanley Mandelstam (1928–2016) was one of the most influential and respected particle theorists. Coming as a young chemical engineer from South Africa to study theoretical physics in England, he quickly became a leading physicist in his field. With his deep understanding of quantum field theory, he pioneered the development of the analytic S-matrix theory as well as the path-dependent formulations for quantum gauge theories and for quantum general relativity. They are being actively used for the electroweak theory and having their imprints in lattice gauge theory and loop quantum gravity. Also he elucidated the mechanisms for quark confinement in quantum chromodynamics, constructed non-perturbative bosonization methods in 1+1 dimensions, and proved the perturbative finiteness and β=0 of N=4 supersymmetric Yang–Mills theory. His work also led to the discovery of dual resonance models, which in turn became superstring theory. He was a leader in these developments, devoting much of his later years to the proof that the theory is perturbatively finite so it can be considered as a contender for the theory of quantum gravity. He was also a very modest and friendly man, impressing everyone with his sharp intellect as well as his humanity. This volume contains essays written by many of his friends and students, including both detailed reports on his scientific achievements as well as personal reminiscences. Also collected in the volume are some selected reprints of Mandelstam's early seminal papers and abstracts of selected papers representing the full spectrum of his contributions. Contents: Recollections of Stanley Mandelstam (Geoffrey Chew) Scientific Biography of Stanley Mandelstam: 1955–1980 (Charles B Thorn) Scientific Biography of Stanley Mandelstam: 1981–2016 (Nathan Berkovits) Stanley Mandelstam: Brief Biography and Selected Publications with Commentary (Ling-Lie Chau) Stanley Mandelstam: The Early Years at a 'Most Stimulating Theoretical Group' (Sabine Lee) The Guiding Influence of Stanley Mandelstam, from S-Matrix Theory to String Theory (Peter Goddard) Remembering Stanley: From a Source of Inspiration to a Fair Strong Competitor (G Veneziano) Stanley Mandelstam and Me and Life on the Light-cone (Lars Brink) Reminiscences of Stanley Mandelstam (John H Schwarz) Stanley Mandelstam and My Postdoctoral Years at Berkeley (Steven Frautschi) Reminiscences on Stanley Mandelstam (Korkut Bardakci) Remembering a Gentle Giant of Physics (Charles Sommerfield) Grad School with Stanley Mandelstam (Joseph Polchinski) Remembering a Gentle Giant of Physics (Mary K Gaillard) Mandelstam & NAL (Pierre Ramond) The Influence of Stanley Mandelstam (Michael B Green) My Interaction with Stanley Mandelstam (Paolo Di Vecchia) My Advisor Stanley (Sang-Jin Sin) Stanley Mandelstam My Graduate Supervisor (Arjun Berera) Reprints and Abstracts of Selected Publications: The Mandelstam Representations in the Mandelstam Variables for S-Matrices: Determination of the Pion-Nucleon Scattering Amplitude from Dispersion Relations and Unitarity. General Theory Analytic Properties of Transition Amplitudes in Perturbation Theory Two-Dimensional Representations of Scattering Amplitudes and Their Applications The S-Matrix Approach: Theory of Low-Energy Pion–Pion Interactions Dispersion Relations in Strong-Coupling Physics The Mandelstam Path-Field Formulation for Quantum Gauge Theories and Feynman Rules: Quantum Electrodynamics Without Potentia
Author : Lars Brink,Richard C Brower,Carleton Detar,Chung-i Tan,Kok Khoo Phua
Publisher : World Scientific
Page : 319 pages
File Size : 45,6 Mb
Release : 2021-12-02
Category : Science
ISBN : 9789811219849
This special volume is dedicated to Geoffrey Chew who passed away on April 12, 2019, at age 94. He is best known as the architect and passionate champion of the bootstrap concept, sometimes called nuclear democracy. His work influenced generations of particle physicists. His passion for physics was an inspiration for his many students and associates. From the Chew-Low theory for meson-nucleon scattering to Analytic S-Matrix, Regge Poles, and Bootstrap principle, his originality left its mark in ways that continue to the present. With contributions from Chew's former collaborators, students, and friends, the book will cover various facets of his life and impact on physics.Contributors include Steven Weinberg, Steven Frautschi, Gabriele Veneziano, Peter Landshoff, Carl Rosenzweig, Basarab Nicolescu, William Frazer, David Gross, John Schwartz, Ling-Lie Chau, Chung-I Tan, Richard Brower, Carleton DeTar, R Shankar, David Kaiser, Fritjof Capra, and others.
Author : Victor Gorbenko
Publisher : Springer
Page : 133 pages
File Size : 49,8 Mb
Release : 2016-09-21
Category : Science
ISBN : 9783319446035
This thesis studies various aspects of non-critical strings both as an example of a non-trivial and solvable model of quantum gravity and as a consistent approximation to the confining flux tube in quantum chromodynamics (QCD). It proposes and develops a new technique for calculating the finite volume spectrum of confining flux tubes. This technique is based on approximate integrability and it played a game-changing role in the study of confining strings. Previously, a theoretical interpretation of available high quality lattice data was impossible, because the conventional perturbative expansion for calculating the string spectra was badly asymptotically diverging in the regime accessible on the lattice. With the new approach, energy levels can be calculated for much shorter flux tubes than was previously possible, allowing for a quantitative comparison with existing lattice data. The improved theoretical control makes it manifest that existing lattice data provides strong evidence for a new pseudoscalar particle localized on the QCD fluxtube - the worldsheet axion. The new technique paves a novel and promising path towards understanding the dynamics of quark confinement.
Author : Anonim
Publisher : Unknown
Page : 648 pages
File Size : 53,9 Mb
Release : 1964
Category : American literature
ISBN : UCSC:32106020974991
Author : Holmfridur Sigridar Hannesdottir,Sebastian Mizera
Publisher : Springer Nature
Page : 165 pages
File Size : 43,8 Mb
Release : 2023-01-01
Category : Science
ISBN : 9783031182587
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 : Richard John Eden
Publisher : CUP Archive
Page : 474 pages
File Size : 50,9 Mb
Release : 1981
Category : Business & Economics
ISBN : 0521281601
Author : Michael Reed,Barry Simon
Publisher : Elsevier
Page : 463 pages
File Size : 40,5 Mb
Release : 1979-05-29
Category : Mathematics
ISBN : 9780080925387
Scattering theory is the study of an interacting system on a scale of time and/or distance which is large compared to the scale of the interaction itself. As such, it is the most effective means, sometimes the only means, to study microscopic nature. To understand the importance of scattering theory, consider the variety of ways in which it arises. First, there are various phenomena in nature (like the blue of the sky) which are the result of scattering. In order to understand the phenomenon (and to identify it as the result of scattering) one must understand the underlying dynamics and its scattering theory. Second, one often wants to use the scattering of waves or particles whose dynamics on knows to determine the structure and position of small or inaccessible objects. For example, in x-ray crystallography (which led to the discovery of DNA), tomography, and the detection of underwater objects by sonar, the underlying dynamics is well understood. What one would like to construct are correspondences that link, via the dynamics, the position, shape, and internal structure of the object to the scattering data. Ideally, the correspondence should be an explicit formula which allows one to reconstruct, at least approximately, the object from the scattering data. The main test of any proposed particle dynamics is whether one can construct for the dynamics a scattering theory that predicts the observed experimental data. Scattering theory was not always so central the physics. Even thought the Coulomb cross section could have been computed by Newton, had he bothered to ask the right question, its calculation is generally attributed to Rutherford more than two hundred years later. Of course, Rutherford's calculation was in connection with the first experiment in nuclear physics.
Author : Rafael Delgado López
Publisher : Springer
Page : 197 pages
File Size : 52,5 Mb
Release : 2017-06-29
Category : Science
ISBN : 9783319604985
In this dissertation, we revisit the prospects of a strongly interacting theory for the Electroweak Symmetry Breaking Sector of the Standard Model, after the discovery of a Higgs-like boson at 125GeV. As the LHC constrains new phenomena near the Higgs mass, it is natural to assume that the new scale is of order 1TeV. This mass gap might indicate strongly interacting new physics. This work is of quite general validity and model independence. With only a few parameters at the Lagrangian level, multiple channels (possibly with new physics resonances) are describable, and many BSM theories can be treated. It will be of interest to postgraduate students and researchers, and is accessible to newcomers in the field. Many calculations are given in full detail and there are ample graphical illustrations.
