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Ordered Exponential Fields
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Book Synopsis Ordered Exponential Fields by : Salma Kuhlmann
Download or read book Ordered Exponential Fields written by Salma Kuhlmann and published by American Mathematical Soc.. This book was released on 2000 with total page 186 pages. Available in PDF, EPUB and Kindle. Book excerpt: Model theoretic algebra has witnessed remarkable progress in the last few years. It has found profound applications in other areas of mathematics, notably in algebraic geometry and in singularity theory. Since Wilkie's results on the o-minimality of the expansion of the reals by the exponential function, and most recently even by all Pfaffian functions, the study of o-minimal expansions of the reals has become a fascinating topic. The quest for analogies between the semi-algebraic case and the o-minimal case has set a direction to this research. Through the Artin-Schreier Theory of real closed fields, the structure of the non-archimedean models in the semi-algebraic case is well understood. For the o-minimal case, so far there has been no systematic study of the non-archimedean models. The goal of this monograph is to serve this purpose. The author presents a detailed description of the non-archimedean models of the elementary theory of certain o-minimal expansions of the reals in which the exponential function is definable. The example of exponential Hardy fields is worked out with particular emphasis. The basic tool is valuation theory, and a sufficient amount of background material on orderings and valuations is presented for the convenience of the reader.
Book Synopsis Real Algebraic Geometry and Ordered Structures by : Charles N. Delzell
Download or read book Real Algebraic Geometry and Ordered Structures written by Charles N. Delzell and published by American Mathematical Soc.. This book was released on 2000 with total page 320 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains 16 carefully refereed articles by participants in the Special Semester and the AMS Special Session on Real Algebraic Geometry and Ordered Structures held at Louisiana State University and Southern University (Baton Rouge). The 23 contributors to this volume were among the 75 mathematicians from 15 countries who participated in the special semester. Topics include the topology of real algebraic curves (Hilbert's 16th problem), moduli of real algebraic curves, effective sums of squares of real forms (Hilbert's 17th problem), efficient real quantifier elimination, subanalytic sets and stratifications, semialgebraic singularity theory, radial vector fields, exponential functions and valuations on nonarchimedean ordered fields, valued field extensions, partially ordered and lattice-ordered rings, rings of continuous functions, spectra of rings, and abstract spaces of (higher-level) orderings and real places. This volume provides a good overview of the state of the art in this area in the 1990s. It includes both expository and original research papers by top workers in this thriving field. The authors and editors strived to make the volume useful to a wide audience (including students and researchers) interested in real algebraic geometry and ordered structures-two subjects that are obviously related, but seldom brought together.
Book Synopsis Ordered Algebraic Structures and Related Topics by : Fabrizio Broglia
Download or read book Ordered Algebraic Structures and Related Topics written by Fabrizio Broglia and published by American Mathematical Soc.. This book was released on 2017 with total page 390 pages. Available in PDF, EPUB and Kindle. Book excerpt: Contains the proceedings of the international conference "Ordered Algebraic Structures and Related Topics", held in October 2015, at CIRM, Luminy, Marseilles. Papers cover topics in real analytic geometry, real algebra, and real algebraic geometry including complexity issues, model theory of various algebraic and differential structures, Witt equivalence of fields, and the moment problem.
Book Synopsis The Classical Fields by : H. Salzmann
Download or read book The Classical Fields written by H. Salzmann and published by Cambridge University Press. This book was released on 2007-08-23 with total page 418 pages. Available in PDF, EPUB and Kindle. Book excerpt: The real, rational, complex and p-adic numbers are discussed in detail in this comprehensive work.
Book Synopsis Green's Functions and Ordered Exponentials by : H. M. Fried
Download or read book Green's Functions and Ordered Exponentials written by H. M. Fried and published by Cambridge University Press. This book was released on 2002-10-10 with total page 183 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents a functional approach to the construction, use and approximation of Green's functions and their associated ordered exponentials. After a brief historical introduction, the author discusses new solutions to problems involving particle production in crossed laser fields and non-constant electric fields. Applications to problems in potential theory and quantum field theory are covered, along with approximations for the treatment of color fluctuations in high-energy QCD scattering, and a model for summing classes of eikonal graphs in high-energy scattering problems. The book also presents a variant of the Fradkin representation which suggests a new non-perturbative approximation scheme, and provides a qualitative measure of the error involved in each such approximation. Covering the basics as well as more advanced applications, this book is suitable for graduate students and researchers in a wide range of fields, including quantum field theory, fluid dynamics and applied mathematics.
Book Synopsis Handbook of the History and Philosophy of Mathematical Practice by : Bharath Sriraman
Download or read book Handbook of the History and Philosophy of Mathematical Practice written by Bharath Sriraman and published by Springer Nature. This book was released on with total page 3221 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Field Theory written by Pierre Ramond and published by Routledge. This book was released on 2020-09-29 with total page 345 pages. Available in PDF, EPUB and Kindle. Book excerpt: Presents recent advances of perturbative relativistic field theory in a pedagogical and straightforward way. For graduate students who intend to specialize in high-energy physics.
Book Synopsis Quantum Field Theory by : Eduardo Fradkin
Download or read book Quantum Field Theory written by Eduardo Fradkin and published by Princeton University Press. This book was released on 2021-03-23 with total page 754 pages. Available in PDF, EPUB and Kindle. Book excerpt: "Quantum field theory is the mathematical and conceptual framework that describes the physics of the very small, including subatomic particles and quasiparticles. It is used to address a range of problems across subfields, from high-energy physics and gravitation to statistical physics and condensed matter physics. Despite the breadth of its applications, however, the teaching of quantum field theory has historically been strongly oriented toward high-energy physics students, while others-particularly in condensed matter and statistical physics-are typically taught in a separate course, or take an alternate sequence in many-body and statistical physics. Author Eduardo Fradkin strongly believes that this separation is both artificial and detrimental to all groups' understanding of quantum field theory. This textbook, developed from a graduate course Fradkin has taught for decades at the University of Illinois, offers a new, "multicultural" approach to the subject that seeks to remedy this fragmentation. It covers both basic techniques and topics at the frontiers of current research, and integrates modern concepts and examples from high-energy, statistical, and condensed-matter physics alike. Extensive problem sets further illustrate applications across a range of subfields. The book will be suitable for students across physical subdisciplines who have mastered graduate-level quantum mechanics, and will be a useful reference for researchers"--
Book Synopsis Structural Aspects Of Quantum Field Theory (In 2 Volumes) by : Gerhard Grensing
Download or read book Structural Aspects Of Quantum Field Theory (In 2 Volumes) written by Gerhard Grensing and published by World Scientific. This book was released on 2013-05-21 with total page 1596 pages. Available in PDF, EPUB and Kindle. Book excerpt: 'The book is primarily addressed to physicists. Nevertheless, as numerous examples are known in which exploration of the land where physics and mathematics overlap (and which quantum field theory definitely belongs to) resulted in important developments in mathematics, many mathematicians may also find this book interesting and even inspiring.'MathSciNetThis book is devoted to the subject of quantum field theory. It is divided into two volumes. The first can serve as a textbook on the main techniques and results of quantum field theory, while the second treats more recent developments, in particular the subject of quantum groups and noncommutative geometry, and their interrelation.The first volume is directed at graduate students who want to learn the basic facts about quantum field theory. It begins with a gentle introduction to classical field theory, including the standard model of particle physics, general relativity, and also supergravity. The transition to quantized fields is performed with path integral techniques, by means of which the one-loop renormalization of a self-interacting scalar quantum field, of quantum electrodynamics, and the asymptotic freedom of quantum chromodynamics is treated. In the last part of the first volume, the application of path integral methods to systems of quantum statistical mechanics is covered. The book ends with a rather detailed investigation of the fractional quantum Hall effect, and gives a stringent derivation of Laughlin's trial ground state wave function as an exact ground state.The second volume covers more advanced themes. In particular Connes' noncommutative geometry is dealt with in some considerable detail; the presentation attempts to acquaint the physics community with the substantial achievements that have been reached by means of this approach towards the understanding of the elusive Higgs particle. The book also covers the subject of quantum groups and its application to the fractional quantum Hall effect, as it is for this paradigmatic physical system that noncommutative geometry and quantum groups can be brought together.
Book Synopsis Integrability: From Statistical Systems to Gauge Theory by : Patrick Dorey
Download or read book Integrability: From Statistical Systems to Gauge Theory written by Patrick Dorey and published by Oxford University Press. This book was released on 2019-07-24 with total page 608 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume, 106 of the Les Houches Summer School series, brings together applications of integrability to supersymmetric gauge and string theory. The book focuses on the application of integrability and problems in quantum field theory. Particular emphasis is given to the exact solution of planar N=4 super-Yang-Mills theory and its relation with string theory on the one hand, and the exact determination of the low-energy physics of N=2 super-Yang-Mills theories on the other; links with other domains are also explored. The purpose of the Les Houches Summer School was to bring together young researchers and specialists from statistical physics, condensed matter physics, gauge and string theory, and mathematics, to stimulate discussion across these different research areas.
Book Synopsis Non-perturbative Methods in 2 Dimensional Quantum Field Theory by : Elcio Abdalla
Download or read book Non-perturbative Methods in 2 Dimensional Quantum Field Theory written by Elcio Abdalla and published by World Scientific. This book was released on 2001 with total page 834 pages. Available in PDF, EPUB and Kindle. Book excerpt: The second edition of Non-Perturbative Methods in Two-Dimensional Quantum Field Theory is an extensively revised version, involving major changes and additions. Although much of the material is special to two dimensions, the techniques used should prove helpful also in the development of techniques applicable in higher dimensions. In particular, the last three chapters of the book will be of direct interest to researchers wanting to work in the field of conformal field theory and strings.This book is intended for students working for their PhD degree and post-doctoral researchers wishing to acquaint themselves with the non-perturbative aspects of quantum field theory.
Book Synopsis Topological and Non-Topological Solitons in Scalar Field Theories by : Yakov M. Shnir
Download or read book Topological and Non-Topological Solitons in Scalar Field Theories written by Yakov M. Shnir and published by Cambridge University Press. This book was released on 2018-07-26 with total page 281 pages. Available in PDF, EPUB and Kindle. Book excerpt: Solitons emerge in various non-linear systems as stable localized configurations, behaving in many ways like particles, from non-linear optics and condensed matter to nuclear physics, cosmology and supersymmetric theories. This book provides an introduction to integrable and non-integrable scalar field models with topological and non-topological soliton solutions. Focusing on both topological and non-topological solitons, it brings together debates around solitary waves and construction of soliton solutions in various models and provides a discussion of solitons using simple model examples. These include the Kortenweg-de-Vries system, sine-Gordon model, kinks and oscillons, and skyrmions and hopfions. The classical field theory of scalar field in various spatial dimensions is used throughout the book in presentation of related concepts, both at the technical and conceptual level. Providing a comprehensive introduction to the description and construction of solitons, this book is ideal for researchers and graduate students in mathematics and theoretical physics.
Book Synopsis Quantum Field Theory by : François Gelis
Download or read book Quantum Field Theory written by François Gelis and published by Cambridge University Press. This book was released on 2019-07-11 with total page 611 pages. Available in PDF, EPUB and Kindle. Book excerpt: A rigorous and self-contained text reviewing the fundamentals of quantum field theory and exploring advanced topics and modern techniques.
Book Synopsis Logic Colloquium '84 by : J.B. Paris
Download or read book Logic Colloquium '84 written by J.B. Paris and published by Elsevier. This book was released on 2011-10-10 with total page 389 pages. Available in PDF, EPUB and Kindle. Book excerpt: This proceedings volume contains most of the invited talks presented at the colloquium. The main topics treated are the model theory of arithmetic and algebra, the semantics of natural languages, and applications of mathematical logic to complexity theory. The volume contains both surveys by acknowledged experts and original research papers presenting advances in these disciplines.
Book Synopsis Quantum Field Theory Of Point Particles And Strings by : Brian Hatfield
Download or read book Quantum Field Theory Of Point Particles And Strings written by Brian Hatfield and published by CRC Press. This book was released on 2018-03-09 with total page 474 pages. Available in PDF, EPUB and Kindle. Book excerpt: First Published in 2018. The emphasis of the book is calculational, and most computations are presented in step-by-step detail. The book is unique in that it develops all three representations of quantum field theory (operator, functional Schr dinger, and path integral) for point particles and strings. In many cases, identical results are worked out in each representation to emphasize the representation-independent structures of quantum field theory
Book Synopsis Modern Functional Quantum Field Theory: Summing Feynman Graphs by : Herbert Martin Fried
Download or read book Modern Functional Quantum Field Theory: Summing Feynman Graphs written by Herbert Martin Fried and published by World Scientific. This book was released on 2014-01-10 with total page 281 pages. Available in PDF, EPUB and Kindle. Book excerpt: These pages offer a simple, analytic, functional approach to non-perturbative QFT, using a frequently overlooked functional representation of Fradkin to explicitly calculate relevant portions of the Schwinger Generating Functional (GF). In QED, this corresponds to summing all Feynman graphs representing virtual photon exchange between charged particles. It is then possible to see, analytically, the cancellation of an infinite number of perturbative, UV logarithmic divergences, leading to an approximate but most reasonable statement of finite charge renormalization.A similar treatment of QCD, with the addition of a long-overlooked but simple rearrangement of the Schwinger GF which displays Manifest Gauge Invariance, is then able to produce a simple, analytic derivation of quark-binding potentials without any approximation of infinite quark masses. A crucial improvement of previous QCD theory takes into account the experimental fact that asymptotic quarks are always found in bound states; and therefore that their transverse coordinates can never be measured, nor specified, exactly. And this change of formalism permits a clear and simple realization of true quark binding, into mesons and nucleons. An extension into the QCD binding of two nucleons into an effective deuteron presents a simple, analytic derivation of nuclear forces.Finally, a new QED-based solution of Vacuum Energy is displayed as a possible candidate for Dark Energy. An obvious generalization to include Inflation, which automatically suggests a model for Dark Matter, is immediately possible; and one more obvious generalization produces an understanding of the origin of the Big Bang, and of the Birth (and Death) of a Universe. If nothing else, this illustrates the Power and the Reach of Quantum Field Theory.
Author :Heinz-Dieter Ebbinghaus Publisher :Springer Science & Business Media ISBN 13 :3662090589 Total Pages :653 pages Book Rating :4.6/5 (62 download)
Book Synopsis Ω-Bibliography of Mathematical Logic by : Heinz-Dieter Ebbinghaus
Download or read book Ω-Bibliography of Mathematical Logic written by Heinz-Dieter Ebbinghaus and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 653 pages. Available in PDF, EPUB and Kindle. Book excerpt: Gert H. Müller The growth of the number of publications in almost all scientific areas, as in the area of (mathematical) logic, is taken as a sign of our scientifically minded culture, but it also has a terrifying aspect. In addition, given the rapidly growing sophistica tion, specialization and hence subdivision of logic, researchers, students and teachers may have a hard time getting an overview of the existing literature, partic ularly if they do not have an extensive library available in their neighbourhood: they simply do not even know what to ask for! More specifically, if someone vaguely knows that something vaguely connected with his interests exists some where in the literature, he may not be able to find it even by searching through the publications scattered in the review journals. Answering this challenge was and is the central motivation for compiling this Bibliography. The Bibliography comprises (presently) the following six volumes (listed with the corresponding Editors): I. Classical Logic W. Rautenberg 11. Non-classical Logics W. Rautenberg 111. Model Theory H.-D. Ebbinghaus IV. Recursion Theory P.G. Hinman V. Set Theory A.R. Blass VI. ProofTheory; Constructive Mathematics J.E. Kister; D. van Dalen & A.S. Troelstra.
