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Combinatorics And Renormalization In Quantum Field Theory
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Book Synopsis Combinatorics And Renormalization In Quantum Field Theory by : E.r. Caianiello
Download or read book Combinatorics And Renormalization In Quantum Field Theory written by E.r. Caianiello and published by Westview Press. This book was released on 2003-04-17 with total page 144 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is based upon work done by the author and his collaborators over a period of approximately twenty years and is dedicated to some selected topics of quantum field theory, which have proved of increasing importance with the passing of time.There are three parts: Combinatoric Methods Equations for Green's Functions and Perturbative Expansions Regularization, Renormalization, and Mass Equations This work will be useful to anyone interested in learning or using quantum field theory, many-body physics and, as well, to many applied mathematicians, because it introduces a number of combinatoric and analytic tools which drastically simplify, and at times bypass, treatments which customarily take up most of the bulk of the standard texts.
Book Synopsis Combinatorics and Renormalization in Quantum Field Theory by : Eduardo R. Caianiello
Download or read book Combinatorics and Renormalization in Quantum Field Theory written by Eduardo R. Caianiello and published by Addison Wesley Longman. This book was released on 1973 with total page 150 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Combinatorial Physics by : Adrian Tanasa
Download or read book Combinatorial Physics written by Adrian Tanasa and published by Oxford University Press. This book was released on 2021 with total page 409 pages. Available in PDF, EPUB and Kindle. Book excerpt: The goal of the book is to use combinatorial techniques to solve fundamental physics problems, and vice-versa, to use theoretical physics techniques to solve combinatorial problems.
Book Synopsis A Combinatorial Perspective on Quantum Field Theory by : Karen Yeats
Download or read book A Combinatorial Perspective on Quantum Field Theory written by Karen Yeats and published by Springer. This book was released on 2016-11-23 with total page 120 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Combinatorics and Physics by : Kurusch Ebrahimi-Fard
Download or read book Combinatorics and Physics written by Kurusch Ebrahimi-Fard and published by American Mathematical Soc.. This book was released on 2011 with total page 480 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is based on the mini-workshop Renormalization, held in December 2006, and the conference Combinatorics and Physics, held in March 2007. Both meetings took place at the Max-Planck-Institut fur Mathematik in Bonn, Germany. Research papers in the volume provide an overview of applications of combinatorics to various problems, such as applications to Hopf algebras, techniques to renormalization problems in quantum field theory, as well as combinatorial problems appearing in the context of the numerical integration of dynamical systems, in noncommutative geometry and in quantum gravity. In addition, it contains several introductory notes on renormalization Hopf algebras, Wilsonian renormalization and motives.
Book Synopsis New Developments in Quantum Field Theory by : Poul Henrik Damgaard
Download or read book New Developments in Quantum Field Theory written by Poul Henrik Damgaard and published by Springer Science & Business Media. This book was released on 2006-04-11 with total page 360 pages. Available in PDF, EPUB and Kindle. Book excerpt: Quantum field theory is one of most central constructions in 20th century th- retical physics, and it continues to develop rapidly in many different directions. The aim of the workshop “New Developments in Quantum Field Theory”, which was held in Zakopane, Poland, June 14-20, 1997, was to capture a broad selection of the most recent advances in this field. The conference was sponsored by the Scientific and - vironmental Affairs Division of NATO, as part of the Advanced Research Workshop series. This book contains the proceedings of that meeting. Major topics covered at the workshop include quantized theories of gravity, string theory, conformal field theory, cosmology, field theory approaches to critical phenomena and the renormalization group, matrix models, and field theory techniques applied to the theory of turbulence. One common theme at the conference was the use of large-Nmatrix models to obtain exact results in a variety of different disciplines. For example, it has been known for several years that by taking a suitable double-scaling limit, certain string theories (or two-dimensional quantum gravity coupled to matter) can be re-obtained from the large-Nexpansion of matrix models. There continues to be a large activity in this area of research, which was well reflected by talks given at our workshop. Remarkably, large- Nmatrix models have very recently – just a few months before our meeting – been shown to have yet another deep relation to string theory.
Book Synopsis Quantum Fields and Processes by : John Gough
Download or read book Quantum Fields and Processes written by John Gough and published by Cambridge University Press. This book was released on 2018-04-12 with total page 341 pages. Available in PDF, EPUB and Kindle. Book excerpt: Do quantum field theory without Feynman diagrams! Use the combinatorics behind cumulants, correlations, Green's functions and quantum fields.
Book Synopsis Wavelets And Renormalization by : Guy Battle
Download or read book Wavelets And Renormalization written by Guy Battle and published by World Scientific. This book was released on 1999-03-03 with total page 588 pages. Available in PDF, EPUB and Kindle. Book excerpt: WAVELETS AND RENORMALIZATION describes the role played by wavelets in Euclidean field theory and classical statistical mechanics. The author begins with a stream-lined introduction to quantum field theory from a rather basic point of view. Functional integrals for imaginary-time-ordered expectations are introduced early and naturally, while the connection with the statistical mechanics of classical spin systems is introduced in a later chapter.A vastly simplified (wavelet) version of the celebrated Glimm-Jaffe construction of the Φ43 quantum field theory is presented. It is due to Battle and Federbush, and it bases an inductively defined cluster expansion on a wavelet decomposition of the Euclidean quantum field. The presentation is reserved for the last chapter, while the more basic aspects of cluster expansions are reviewed in the chapter on classical spin systems.Wavelets themselves are studied from two different points of view arising from two disciplines. The mathematical point of view covers the basic properties of wavelets and methods for constructing well-known wavelets such as Meyer wavelets, Daubechies wavelets, etc. The physical point of view covers the renormalization group formalism, where there is a close connection between wavelets and Gaussian fixed points.The book is heavily mathematical, but avoids the theorem-proof-theorem-proof format in the interests of preserving the flow of the discussion — i.e., it is written in the style of an old-fashioned theoretical physics book, but the major claims are rigorously proven. The minor themes of the book are reflection positivity, the combinatorics of cluster expansions, and the issue of phase transitions — themes which have nothing to do with wavelets, but which provide necessary cultural background for the physical context.
Book Synopsis Renormalized Quantum Field Theory by : O.I. Zavialov
Download or read book Renormalized Quantum Field Theory written by O.I. Zavialov and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 537 pages. Available in PDF, EPUB and Kindle. Book excerpt: 'Et moi. ... - Ii j'avait su CClIIIIIIaIt CD 1'CVCDir, ODe scmcc matbcmatK:s bas I'CIIdcRd!be je D', semis paiDt ~. humaD mcc. It bas put common sease bact Jules Vcmc 'WIIcR it bdoDp, 011!be topmost sbdl JlCXt 10!be dully c:uista' t.bdlcd 'cIiIc:arded DOlI- The series is diverpt; therefore we may be sense'. Eric T. BcII able 10 do sometbiD & with it O. Heavilide Mathematics is a tool for thought. A highly ncceuary tool in a world where both feedback and non- 1inearities abound. Similarly, all kinds of parts of mathematics serve as tools for other parts and for other sciences. Applying a simple rewriting rule to the quote on the right above one finds such statements as: 'One service topology has rendered mathematical physics .. .'; 'One service logic has rendered com puter science .. .'; 'One service category theory has rendered mathematics .. .'. All arguably true. And all statements obtainable this way form part of the l'Iison d'etre of this series.
Book Synopsis Renormalization Group and Fixed Points by : Timothy J Hollowood
Download or read book Renormalization Group and Fixed Points written by Timothy J Hollowood and published by Springer Science & Business Media. This book was released on 2013-03-28 with total page 78 pages. Available in PDF, EPUB and Kindle. Book excerpt: This Brief presents an introduction to the theory of the renormalization group in the context of quantum field theories of relevance to particle physics. Emphasis is placed on gaining a physical understanding of the running of the couplings. The Wilsonian version of the renormalization group is related to conventional perturbative calculations with dimensional regularization and minimal subtraction. An introduction is given to some of the remarkable renormalization group properties of supersymmetric theories.
Book Synopsis Universality and Renormalization by : Ilia Binder
Download or read book Universality and Renormalization written by Ilia Binder and published by American Mathematical Soc.. This book was released on 2007 with total page 414 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book covers a wide range of phenomena in the natural sciences dominated by notions of universality and renormalization. The contributions in this volume are equally broad in their approach to these phenomena, offering the mathematical as well as the perspective of the applied sciences. They explore renormalization theory in quantum field theory and statistical physics, and its connections to modern mathematics as well as physics on scales from the microscopic to the macroscopic. Information for our distributors: Titles in this series are co-published with the Fields Institute for Research in Mathematical Sciences (Toronto, Ontario, Canada).
Book Synopsis Combinatorial Physics by : Adrian Tanasa
Download or read book Combinatorial Physics written by Adrian Tanasa and published by Oxford University Press. This book was released on 2021-04-16 with total page 420 pages. Available in PDF, EPUB and Kindle. Book excerpt: The interplay between combinatorics and theoretical physics is a recent trend which appears to us as particularly natural, since the unfolding of new ideas in physics is often tied to the development of combinatorial methods, and, conversely, problems in combinatorics have been successfully tackled using methods inspired by theoretical physics. We can thus speak nowadays of an emerging domain of Combinatorial Physics. The interference between these two disciplines is moreover an interference of multiple facets. Its best known manifestation (both to combinatorialists and theoretical physicists) has so far been the one between combinatorics and statistical physics, as statistical physics relies on an accurate counting of the various states or configurations of a physical system. But combinatorics and theoretical physics interact in various other ways. This book is mainly dedicated to the interactions of combinatorics (algebraic, enumerative, analytic) with (commutative and non-commutative) quantum field theory and tensor models, the latter being seen as a quantum field theoretical generalisation of matrix models.
Book Synopsis Graphs in Perturbation Theory by : Michael Borinsky
Download or read book Graphs in Perturbation Theory written by Michael Borinsky and published by Springer. This book was released on 2018-11-04 with total page 173 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is the first systematic study of graphical enumeration and the asymptotic algebraic structures in perturbative quantum field theory. Starting with an exposition of the Hopf algebra structure of generic graphs, it reviews and summarizes the existing literature. It then applies this Hopf algebraic structure to the combinatorics of graphical enumeration for the first time, and introduces a novel method of asymptotic analysis to answer asymptotic questions. This major breakthrough has combinatorial applications far beyond the analysis of graphical enumeration. The book also provides detailed examples for the asymptotics of renormalizable quantum field theories, which underlie the Standard Model of particle physics. A deeper analysis of such renormalizable field theories reveals their algebraic lattice structure. The pedagogical presentation allows readers to apply these new methods to other problems, making this thesis a future classic for the study of asymptotic problems in quantum fields, network theory and far beyond.
Download or read book Nuclear Science Abstracts written by and published by . This book was released on 1973 with total page 1412 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Periods in Quantum Field Theory and Arithmetic by : José Ignacio Burgos Gil
Download or read book Periods in Quantum Field Theory and Arithmetic written by José Ignacio Burgos Gil and published by Springer Nature. This book was released on 2020-03-14 with total page 631 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is the outcome of research initiatives formed during the special ``Research Trimester on Multiple Zeta Values, Multiple Polylogarithms, and Quantum Field Theory'' at the ICMAT (Instituto de Ciencias Matemáticas, Madrid) in 2014. The activity was aimed at understanding and deepening recent developments where Feynman and string amplitudes on the one hand, and periods and multiple zeta values on the other, have been at the heart of lively and fruitful interactions between theoretical physics and number theory over the past few decades. In this book, the reader will find research papers as well as survey articles, including open problems, on the interface between number theory, quantum field theory and string theory, written by leading experts in the respective fields. Topics include, among others, elliptic periods viewed from both a mathematical and a physical standpoint; further relations between periods and high energy physics, including cluster algebras and renormalisation theory; multiple Eisenstein series and q-analogues of multiple zeta values (also in connection with renormalisation); double shuffle and duality relations; alternative presentations of multiple zeta values using Ecalle's theory of moulds and arborification; a distribution formula for generalised complex and l-adic polylogarithms; Galois action on knots. Given its scope, the book offers a valuable resource for researchers and graduate students interested in topics related to both quantum field theory, in particular, scattering amplitudes, and number theory.
Book Synopsis Quantum Fields and Processes by : John Gough
Download or read book Quantum Fields and Processes written by John Gough and published by Cambridge University Press. This book was released on 2018-04-12 with total page 342 pages. Available in PDF, EPUB and Kindle. Book excerpt: Wick ordering of creation and annihilation operators is of fundamental importance for computing averages and correlations in quantum field theory and, by extension, in the Hudson–Parthasarathy theory of quantum stochastic processes, quantum mechanics, stochastic processes, and probability. This book develops the unified combinatorial framework behind these examples, starting with the simplest mathematically, and working up to the Fock space setting for quantum fields. Emphasizing ideas from combinatorics such as the role of lattice of partitions for multiple stochastic integrals by Wallstrom–Rota and combinatorial species by Joyal, it presents insights coming from quantum probability. It also introduces a 'field calculus' which acts as a succinct alternative to standard Feynman diagrams and formulates quantum field theory (cumulant moments, Dyson–Schwinger equation, tree expansions, 1-particle irreducibility) in this language. Featuring many worked examples, the book is aimed at mathematical physicists, quantum field theorists, and probabilists, including graduate and advanced undergraduate students.
Book Synopsis Renormalization by : Laurie M. Brown
Download or read book Renormalization written by Laurie M. Brown and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 187 pages. Available in PDF, EPUB and Kindle. Book excerpt: The purpose of this section is to give you a sketch of how quantum field theory works, where Feynman graphs come from and why they are so useful, where the infinities come from, and how we have learned to deal with them without compromising the physical principles involved. I am purposely treating the problem at the level of the 1940s and 1950s, so as to keep the basic ideas clear and avoid the more difficult problems and more sophisticated methods of recent years. I shall relate my discussion simply to quantum electrodynamics (QED) since that is the most familiar case and the case that was in the forefront from the beginning (though in fact I shall ignore many of the special complications that have to be dealt with when you quantize a gauge field). The methods I shall be describing are applicable to all sorts of quantized fields: the detailed factors are different but the structure of the logical development isjust the same. Not surprisingly, though, the renormalization procedure breaks down if the theory in question is nonrenormalizable. Whether nonrenormalizable theories are theories at all is a matter for debate; in any case, they hold no practical interest for physicists since they are essentially unusable. Quantum electrodynamics was devised in 1927 by Dirac, less than a year after the Schrodinger equation appeared and before the Dirac equa tion for the relativistic electron had been invented.
