Download or read book Renormalized Perturbation Theory And Its Optimization By The Principle Of Minimal Sensitivity written by P M Stevenson and published by World Scientific. This book was released on 2022-03-21 with total page 297 pages. Available in PDF, EPUB and Kindle. Book excerpt: The results of renormalized perturbation theory, in QCD and other quantum field theories, are ambiguous at any finite order, due to renormalization-scheme dependence. The perturbative results depend upon extraneous scheme variables, including the renormalization scale, that the exact result cannot depend on. Such 'non-invariant approximations' occur in many other areas of physics, too. The sensible strategy is to find where the approximant is stationary under small variations of the extraneous variables. This general principle is explained and illustrated with various examples. Also dimensional transmutation, RG equations, the essence of renormalization and the origin of its ambiguities are explained in simple terms, assuming little or no background in quantum field theory. The minimal-sensitivity approach leads to 'optimized perturbation theory,' which is developed in detail. Applications to Re⁺e⁻, the infrared limit, and to the optimization of factorized quantities, are also discussed thoroughly.
Download or read book Superinsulators Bose Metals And High tc Superconductors The Quantum Physics Of Emergent Magnetic Monopoles written by Carlo A Trugenberger and published by World Scientific. This book was released on 2022-04-19 with total page 249 pages. Available in PDF, EPUB and Kindle. Book excerpt: In 1931 Dirac showed that topologically quantized single magnetic charges, magnetic monopoles, while classically forbidden in a gauge theory, are allowed alongside electric charges in a quantum theory of electromagnetism. Such topological magnetic excitations are indeed admitted in the spectrum of most grand unified field theories of elementary interactions. Despite 40 years of dedicated search efforts, nonetheless, they have never shown up in any experiment. This, however, does not preclude the possibility of topological magnetic monopoles being realized as excitations in emergent condensed matter states, where they would be much lighter and easier to create.This book is about the physical effects of such emergent magnetic monopoles. These range from a new mechanism for local, strong pairing of electrons possibly relevant for high-T superconductivity, to the formation of a new quantum phase of matter when monopoles condense. In such a condensate the electric interaction becomes extremely strong, so much so that only extended neutral states survive, with the consequence of an infinite resistance, even at finite temperatures. This state, called a superinsulator, is a dual superconductor and has been experimentally detected in various materials. In a superinsulator the electric interaction becomes analogous to the strong interaction holding quarks together in colour-neutral hadrons. Even more interesting is the case when the condensate carries both magnetic and electric charge. The ensuing state has properties that are strikingly reminiscent of the mysterious pseudogap state of high-T superconductors. Magnetic monopoles might thus have been hiding in plain sight where no one was looking for them for a long time.
Download or read book Resummation and Renormalization in Effective Theories of Particle Physics written by Antal Jakovác and published by Springer. This book was released on 2015-11-02 with total page 229 pages. Available in PDF, EPUB and Kindle. Book excerpt: Effective models of strong and electroweak interactions are extensively applied in particle physics phenomenology, and in many instances can compete with large-scale numerical simulations of Standard Model physics. These contexts include but are not limited to providing indications for phase transitions and the nature of elementary excitations of strong and electroweak matter. A precondition for obtaining high-precision predictions is the application of some advanced functional techniques to the effective models, where the sensitivity of the results to the accurate choice of the input parameters is under control and the insensitivity to the actual choice of ultraviolet regulators is ensured. The credibility of such attempts ultimately requires a clean renormalization procedure and an error estimation due to a necessary truncation in the resummation procedure. In this concise primer we discuss systematically and in sufficient technical depth the features of a number of approximate methods, as applied to various effective models of chiral symmetry breaking in strong interactions and the BEH-mechanism of symmetry breaking in the electroweak theory. After introducing the basics of the functional integral formulation of quantum field theories and the derivation of different variants of the equations which determine the n-point functions, the text elaborates on the formulation of the optimized perturbation theory and the large-N expansion, as applied to the solution of these underlying equations in vacuum. The optimisation aspects of the 2PI approximation is discussed. Each of them is presented as a specific reorganisation of the weak coupling perturbation theory. The dimensional reduction of high temperature field theories is discussed from the same viewpoint. The renormalization program is described for each approach in detail and particular attention is paid to the appropriate interpretation of the notion of renormalization in the presence of the Landau singularity. Finally, results which emerge from the application of these techniques to the thermodynamics of strong and electroweak interactions are reviewed in detail.
Download or read book Self Consistency Requirements of the Renormalization Group for Setting the Renormalization Scale written by and published by . This book was released on 2012 with total page 15 pages. Available in PDF, EPUB and Kindle. Book excerpt: In conventional treatments, predictions from fixed-order perturbative QCD calculations cannot be fixed with certainty due to ambiguities in the choice of the renormalization scale as well as the renormalization scheme. In this paper we present a general discussion of the constraints of the renormalization group (RG) invariance on the choice of the renormalization scale. We adopt the RG based equations, which incorporate the scheme parameters, for a general exposition of RG invariance, since they simultaneously express the invariance of physical observables under both the variation of the renormalization scale and the renormalization scheme parameters. We then discuss the self-consistency requirements of the RG, such as reflexivity, symmetry, and transitivity, which must be satisfied by the scale-setting method. The Principle of Minimal Sensitivity (PMS) requires the slope of the approximant of an observable to vanish at the renormalization point. This criterion provides a scheme-independent estimation, but it violates the symmetry and transitivity properties of the RG and does not reproduce the Gell-Mann-Low scale for QED observables. The Principle of Maximum Conformality (PMC) satisfies all of the deductions of the RG invariance - reflectivity, symmetry, and transitivity. Using the PMC, all non-conformal {{u03B2}Ri}-terms (R stands for an arbitrary renormalization scheme) in the perturbative expansion series are summed into the running coupling, and one obtains a unique, scale-fixed, scheme-independent prediction at any finite order. The PMC scales and the resulting finite-order PMC predictions are both to high accuracy independent of the choice of initial renormalization scale, consistent with RG invariance.
Download or read book High Energy Physics Index written by and published by . This book was released on 1984 with total page 624 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Physics Briefs written by and published by . This book was released on 1984 with total page 904 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book The Principles of Deep Learning Theory written by Daniel A. Roberts and published by Cambridge University Press. This book was released on 2022-05-26 with total page 473 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume develops an effective theory approach to understanding deep neural networks of practical relevance.
Download or read book Exact Renormalization Group The Proceedings Of The Workshop written by Alexander Krasnitz and published by World Scientific. This book was released on 1999-08-13 with total page 238 pages. Available in PDF, EPUB and Kindle. Book excerpt: The subject of the exact renormalization group started from pioneering work by Wegner and Houghton in the early seventies and, a decade later, by Polchinski, who formulated the Wilson renormalization group for field theory. In the past decade considerable progress has been made in this field, which includes the development of alternative formulations of the approach and of powerful techniques for solving the exact renormalization group equations, as well as widening of the scope of the exact renormalization group method to include fermions and gauge fields. In particular, two very recent results, namely the manifestly gauge-invariant formulation of the exact renormalization group equation and the proof of the c-theorem in four dimensions, are presented in this volume.
Download or read book Quark gluon Plasma 4 written by Rudolph C. Hwa and published by World Scientific. This book was released on 2010 with total page 450 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a review volume containing articles written by experts on current theoretical topics in the subject of Quark-Gluon Plasma created in heavy-ion collisions at high energy. It is the fourth volume in the series with the same title sequenced numerically. The articles are written in a pedagogical style so that they can be helpful to a wide range of researchers from graduate students to mature physicists who have not worked previously on the subject. A reader should be able to learn from the reviews without having extensive knowledge of the background literature.
Download or read book Information Theory Inference and Learning Algorithms written by David J. C. MacKay and published by Cambridge University Press. This book was released on 2003-09-25 with total page 694 pages. Available in PDF, EPUB and Kindle. Book excerpt: Information theory and inference, taught together in this exciting textbook, lie at the heart of many important areas of modern technology - communication, signal processing, data mining, machine learning, pattern recognition, computational neuroscience, bioinformatics and cryptography. The book introduces theory in tandem with applications. Information theory is taught alongside practical communication systems such as arithmetic coding for data compression and sparse-graph codes for error-correction. Inference techniques, including message-passing algorithms, Monte Carlo methods and variational approximations, are developed alongside applications to clustering, convolutional codes, independent component analysis, and neural networks. Uniquely, the book covers state-of-the-art error-correcting codes, including low-density-parity-check codes, turbo codes, and digital fountain codes - the twenty-first-century standards for satellite communications, disk drives, and data broadcast. Richly illustrated, filled with worked examples and over 400 exercises, some with detailed solutions, the book is ideal for self-learning, and for undergraduate or graduate courses. It also provides an unparalleled entry point for professionals in areas as diverse as computational biology, financial engineering and machine learning.
Download or read book Elements of Causal Inference written by Jonas Peters and published by MIT Press. This book was released on 2017-11-29 with total page 289 pages. Available in PDF, EPUB and Kindle. Book excerpt: A concise and self-contained introduction to causal inference, increasingly important in data science and machine learning. The mathematization of causality is a relatively recent development, and has become increasingly important in data science and machine learning. This book offers a self-contained and concise introduction to causal models and how to learn them from data. After explaining the need for causal models and discussing some of the principles underlying causal inference, the book teaches readers how to use causal models: how to compute intervention distributions, how to infer causal models from observational and interventional data, and how causal ideas could be exploited for classical machine learning problems. All of these topics are discussed first in terms of two variables and then in the more general multivariate case. The bivariate case turns out to be a particularly hard problem for causal learning because there are no conditional independences as used by classical methods for solving multivariate cases. The authors consider analyzing statistical asymmetries between cause and effect to be highly instructive, and they report on their decade of intensive research into this problem. The book is accessible to readers with a background in machine learning or statistics, and can be used in graduate courses or as a reference for researchers. The text includes code snippets that can be copied and pasted, exercises, and an appendix with a summary of the most important technical concepts.
Download or read book Emergent Phenomena in Correlated Matter written by Eva Pavarini and published by Forschungszentrum Jülich. This book was released on 2013 with total page 562 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book The Anomalous Magnetic Moment of the Muon written by Fred Jegerlehner and published by Springer Science & Business Media. This book was released on 2008 with total page 433 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book reviews the present state of knowledge of the anomalous magnetic moment a=(g-2)/2 of the muon. The muon anomalous magnetic moment is one of the most precisely measured quantities in elementary particle physics and provides one of the most stringent tests of relativistic quantum field theory as a fundamental theoretical framework. It allows for an extremely precise check of the standard model of elementary particles and of its limitations.
Download or read book Relativistic Quantum Mechanics and Field Theory written by Franz Gross and published by John Wiley & Sons. This book was released on 2008-07-11 with total page 643 pages. Available in PDF, EPUB and Kindle. Book excerpt: An accessible, comprehensive reference to modern quantum mechanics and field theory. In surveying available books on advanced quantum mechanics and field theory, Franz Gross determined that while established books were outdated, newer titles tended to focus on recent developments and disregard the basics. Relativistic Quantum Mechanics and Field Theory fills this striking gap in the field. With a strong emphasis on applications to practical problems as well as calculations, Dr. Gross provides complete, up-to-date coverage of both elementary and advanced topics essential for a well-rounded understanding of the field. Developing the material at a level accessible even to newcomers to quantum mechanics, the book begins with topics that every physicist should know-quantization of the electromagnetic field, relativistic one body wave equations, and the theoretical explanation of atomic decay. Subsequent chapters prepare readers for advanced work, covering such major topics as gauge theories, path integral techniques, spontaneous symmetry breaking, and an introduction to QCD, chiral symmetry, and the Standard Model. A special chapter is devoted to relativistic bound state wave equations-an important topic that is often overlooked in other books. Clear and concise throughout, Relativistic Quantum Mechanics and Field Theory boasts examples from atomic and nuclear physics as well as particle physics, and includes appendices with background material. It is an essential reference for anyone working in quantum mechanics today.
Download or read book Optimal Control Theory with Applications in Economics written by Thomas A. Weber and published by MIT Press. This book was released on 2011-09-30 with total page 387 pages. Available in PDF, EPUB and Kindle. Book excerpt: A rigorous introduction to optimal control theory, with an emphasis on applications in economics. This book bridges optimal control theory and economics, discussing ordinary differential equations, optimal control, game theory, and mechanism design in one volume. Technically rigorous and largely self-contained, it provides an introduction to the use of optimal control theory for deterministic continuous-time systems in economics. The theory of ordinary differential equations (ODEs) is the backbone of the theory developed in the book, and chapter 2 offers a detailed review of basic concepts in the theory of ODEs, including the solution of systems of linear ODEs, state-space analysis, potential functions, and stability analysis. Following this, the book covers the main results of optimal control theory, in particular necessary and sufficient optimality conditions; game theory, with an emphasis on differential games; and the application of control-theoretic concepts to the design of economic mechanisms. Appendixes provide a mathematical review and full solutions to all end-of-chapter problems. The material is presented at three levels: single-person decision making; games, in which a group of decision makers interact strategically; and mechanism design, which is concerned with a designer's creation of an environment in which players interact to maximize the designer's objective. The book focuses on applications; the problems are an integral part of the text. It is intended for use as a textbook or reference for graduate students, teachers, and researchers interested in applications of control theory beyond its classical use in economic growth. The book will also appeal to readers interested in a modeling approach to certain practical problems involving dynamic continuous-time models.
Download or read book Foundations of Perturbative QCD written by John Collins and published by Cambridge University Press. This book was released on 2011-04-28 with total page 637 pages. Available in PDF, EPUB and Kindle. Book excerpt: Giving an accurate account of the concepts, theorems and their justification, this book is a systematic treatment of perturbative QCD. It relates the concepts to experimental data, giving strong motivations for the methods. Ideal for graduate students starting their work in high-energy physics, it will also interest experienced researchers.
Download or read book Mathematical Reviews written by and published by . This book was released on 1981 with total page 468 pages. Available in PDF, EPUB and Kindle. Book excerpt:
