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 From Perturbative to Constructive Renormalization written by V. Rivasseau and published by Princeton University Press. This book was released on 2014-07-14 with total page 347 pages. Available in PDF, EPUB and Kindle. Book excerpt: The last decade has seen striking progress in the subject of renormalization in quantum field theory. The old subject of perturbative renormalization has been revived by the use of powerful methods such as multiscale decompositions; precise estimates have been added to the initial theorems on finiteness of renormalized perturbation theory, with new results on its large order asymptotics. Furthermore, constructive field theory has reached one of its major goals, the mathematically rigorous construction of some renormalizable quantum field theories. For these models one can in particular investigate rigorously the phenomenon of asymptotic freedom, which plays a key role in our current understanding of the interaction among elementary particles. However, until this book, there has been no pedagogical synthesis of these new developments. Vincent Rivasseau, who has been actively involved in them, now describes them for a wider audience. There are, in fact, common concepts at the heart of the progress on perturbative and constructive techniques. Exploiting these similarities, the author uses perturbative renormalization, which is the more widely known and conceptually simpler of the two cases, to explain the less familiar but more mathematically meaningful constructive renormalization. Originally published in 1991. The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.
Download or read book Algebraic Renormalization written by Olivier Piguet and published by Springer Science & Business Media. This book was released on 2008-09-11 with total page 142 pages. Available in PDF, EPUB and Kindle. Book excerpt: The idea of this book originated from two series of lectures given by us at the Physics Department of the Catholic University of Petr6polis, in Brazil. Its aim is to present an introduction to the "algebraic" method in the perturbative renormalization of relativistic quantum field theory. Although this approach goes back to the pioneering works of Symanzik in the early 1970s and was systematized by Becchi, Rouet and Stora as early as 1972-1974, its full value has not yet been widely appreciated by the practitioners of quantum field theory. Becchi, Rouet and Stora have, however, shown it to be a powerful tool for proving the renormalizability of theories with (broken) symmetries and of gauge theories. We have thus found it pertinent to collect in a self-contained manner the available information on algebraic renormalization, which was previously scattered in many original papers and in a few older review articles. Although we have taken care to adapt the level of this book to that of a po- graduate (Ph. D. ) course, more advanced researchers will also certainly find it useful. The deeper knowledge of renormalization theory we hope readers will acquire should help them to face the difficult problems of quantum field theory. It should also be very helpful to the more phenomenology oriented readers who want to famili- ize themselves with the formalism of renormalization theory, a necessity in view of the sophisticated perturbative calculations currently being done, in particular in the standard model of particle interactions.
Download or read book Non perturbative Renormalization written by Vieri Mastropietro and published by World Scientific. This book was released on 2008 with total page 303 pages. Available in PDF, EPUB and Kindle. Book excerpt: The notion of renormalization is at the core of several spectacular achievements of contemporary physics, and in the last years powerful techniques have been developed allowing to put renormalization on a firm mathematical basis. This book provides a self-consistent and accessible introduction to the sophisticated tools used in the modern theory of non-perturbative renormalization, allowing an unified and rigorous treatment of Quantum Field Theory, Statistical Physics and Condensed Matter models. In particular the first part of this book is devoted to Constructive Quantum Field Theory, providing a mathematical construction of models at low dimensions and discussing the removal of the ultraviolet and infrared cut-off, the verification of the axioms and the validity of Ward Identities with the relative anomalies. The second part is devoted to lattice 2D Statistical Physics, analyzing in particular the theory of universality in perturbed Ising models and the computation of the non-universal critical indices in Vertex or Ashkin-Teller models. Finally the third part is devoted to the analysis of complex quantum fluids showing Luttinger of Fermi liquid behavior, like the 1D or 2D Hubbard model.
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.
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.
Download or read book The Theory of Critical Phenomena written by J. J. Binney and published by Oxford University Press. This book was released on 1992-06-11 with total page 477 pages. Available in PDF, EPUB and Kindle. Book excerpt: The successful calculation of critical exponents for continuous phase transitions is one of the main achievements of theoretical physics over the last quarter-century. This was achieved through the use of scaling and field-theoretic techniques which have since become standard equipment in many areas of physics, especially quantum field theory. This book provides a thorough introduction to these techniques. Continuous phase transitions are introduced, then the necessary statistical mechanics is summarized, followed by standard models, some exact solutions and techniques for numerical simulations. The real-space renormalization group and mean-field theory are then explained and illustrated. The final chapters cover the Landau-Ginzburg model, from physical motivation, through diagrammatic perturbation theory and renormalization to the renormalization group and the calculation of critical exponents above and below the critical temperature.
Download or read book Introduction to a Renormalisation Group Method written by Roland Bauerschmidt and published by Springer Nature. This book was released on 2019-10-16 with total page 283 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a primer on a mathematically rigorous renormalisation group theory, presenting mathematical techniques fundamental to renormalisation group analysis such as Gaussian integration, perturbative renormalisation and the stable manifold theorem. It also provides an overview of fundamental models in statistical mechanics with critical behaviour, including the Ising and φ4 models and the self-avoiding walk. The book begins with critical behaviour and its basic discussion in statistical mechanics models, and subsequently explores perturbative and non-perturbative analysis in the renormalisation group. Lastly it discusses the relation of these topics to the self-avoiding walk and supersymmetry. Including exercises in each chapter to help readers deepen their understanding, it is a valuable resource for mathematicians and mathematical physicists wanting to learn renormalisation group theory.
Download or read book Excluded Volume Effects in Polymer Solutions written by Lothar Schäfer and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 554 pages. Available in PDF, EPUB and Kindle. Book excerpt: Schäfer gives a concise overview of the static equilibrium properties of polymer solutions. In the first part diagrammatic perturbation theory is derived from scratch. The second part illustrates the basic ideas of the renormalization group (RG). The crucial role of dilation invariance is stressed. The more efficient method of dimensional regularization and minimal subtractions is worked out in part three. The fourth part contains a unified evaluation of the theory to the one loop level. All the important experimental quantities are discussed in detail, and the results are compared extensively to experiment. Empirical methods of data analysis are critically discussed. The final (fifth) part is devoted to extensions of theory. The first three parts of this book may serve as the basis of a course. Parts four and five are hoped to be useful for detailed quantitative evaluations of experiments.
Download or read book Renormalization Methods written by W. D. McComb and published by Oxford University Press. This book was released on 2004 with total page 349 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text fills a gap between undergraduate and more advanced texts on quantum field theory. It covers a range of renormalization methods with a clear physical interpretation, proceeds to the epsilon-expansion and ends with the first-order corrections to critical exponents beyond mean-field theory.
Download or read book Renormalized Supersymmetry written by O. Piguet and published by . This book was released on 1986 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
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 Lectures On Phase Transitions And The Renormalization Group written by Nigel Goldenfeld and published by CRC Press. This book was released on 2018-03-08 with total page 313 pages. Available in PDF, EPUB and Kindle. Book excerpt: Covering the elementary aspects of the physics of phases transitions and the renormalization group, this popular book is widely used both for core graduate statistical mechanics courses as well as for more specialized courses. Emphasizing understanding and clarity rather than technical manipulation, these lectures de-mystify the subject and show precisely "how things work." Goldenfeld keeps in mind a reader who wants to understand why things are done, what the results are, and what in principle can go wrong. The book reaches both experimentalists and theorists, students and even active researchers, and assumes only a prior knowledge of statistical mechanics at the introductory graduate level.Advanced, never-before-printed topics on the applications of renormalization group far from equilibrium and to partial differential equations add to the uniqueness of this book.
Download or read book Renormalized Supersymmetry written by PIGUET and published by Springer Science & Business Media. This book was released on 2013-03-08 with total page 360 pages. Available in PDF, EPUB and Kindle. Book excerpt: The present book grew out of lecture notes prepared for a "Cours du troisieme cycle de la Suisse Romande", 1983 in Lausanne. The original notes are considerably extended and brought up to date. In fact the book offers at many instances completely new derivations. Half-way between textbook and research monograph we believe it to be useful for students in elementary particle physics as well as for research workers in the realm of supersymmetry. In writing the book we looked back not only on ten years of super symmetry but also on ten years of our own life and work. We realize how deeply we are indebted to many friends and colleagues. Some shared our efforts, some helped and encouraged us, some provided the facili ties to work. Their list comprises at least C. Becchi, S. Bedding, P. Breitenlohner, T.E. Clark, S. Ferrara, R. Gatto, M. Jacob, W. Lang, J.H. Lowenstein, D. Maison, H. Nicolai, J. Prentki, A. Rouet, H. Ruegg, M. Schweda, R. Stora, J. Wess, W. Zimmermann, B. Zumino. During the last ten years we had the privilege to work at CERN (Geneva), Departement de Physique Theorique (University of Geneva), Institut fUr Theoretische Physik (University of Karlsruhe) and at the Max-Planck-Institut fUr Physik und Astrophysik (Munich) for which we are most grateful. Grate fully acknowledged is also the support we received by "the Swiss National Science Foundation" (O.P.), the "Deutsche Forschungsgemeinschaft" (Heisenberg-Fellowship; K.S.)
Download or read book Statistical Physics of Fields written by Mehran Kardar and published by Cambridge University Press. This book was released on 2007-06-07 with total page 376 pages. Available in PDF, EPUB and Kindle. Book excerpt: While many scientists are familiar with fractals, fewer are familiar with scale-invariance and universality which underlie the ubiquity of their shapes. These properties may emerge from the collective behaviour of simple fundamental constituents, and are studied using statistical field theories. Initial chapters connect the particulate perspective developed in the companion volume, to the coarse grained statistical fields studied here. Based on lectures taught by Professor Kardar at MIT, this textbook demonstrates how such theories are formulated and studied. Perturbation theory, exact solutions, renormalization groups, and other tools are employed to demonstrate the emergence of scale invariance and universality, and the non-equilibrium dynamics of interfaces and directed paths in random media are discussed. Ideal for advanced graduate courses in statistical physics, it contains an integrated set of problems, with solutions to selected problems at the end of the book and a complete set available to lecturers at www.cambridge.org/9780521873413.
Download or read book Causal Perturbation Theory and Differential Renormalization written by and published by . This book was released on 1999 with total page 15 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Field Theoretic Renormalization Group in Fully Developed Turbulence written by L.Ts Adzhemyan and published by CRC Press. This book was released on 1999-03-08 with total page 212 pages. Available in PDF, EPUB and Kindle. Book excerpt: The renormalization group (RG) theory of fully developed hydrodynamical turbulence is a new and developing field of research. This book gives a detailed and comprehensive review of the results obtained using this theory over the past 20 years. The authors have systematically adopted the highly successful field theoretic RG technique, which has a reliable base in the form of quantum- field renormalization theory, involves powerful and convenient methods of calculation such as analytic regularization and minimal subtractions, and allows one to obtain results which are difficult to achieve using other methods. In the first chapter the basic theory and technique are presented, while the next chapter deals with more advanced aspects of the theory, including the critical dimensions of various composite operators, infrared asymptotic behavior of scaling functions, the equation of spectral energy balance, and calculating the amplitudes in scaling laws. The third chapter presents a series of examples, such as turbulent convection of passive scalar admixture, the influence of anisotropy and gyrotropy, magnetohydrodynamical turbulence, and Langmuir turbulence of plasma. In contrast to more established disciplines, such as the theory of critical phenomena, in the RG theory of turbulence there is as yet no unique and generally accepted calculation technique. For this reason the authors also present the necessary information on the renormalization theory of the RG technique, making the subject accessible to a wide range of readers. The book will therefore be a useful source of reference for students and researchers in turbulence, statistical mechanics, and related fields, including those with no prior experience of using quantum-field techniques.
