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Renormalization
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Book Synopsis Renormalization and Effective Field Theory by : Kevin Costello
Download or read book Renormalization and Effective Field Theory written by Kevin Costello and published by American Mathematical Soc.. This book was released on 2011 with total page 264 pages. Available in PDF, EPUB and Kindle. Book excerpt: Quantum field theory has had a profound influence on mathematics, and on geometry in particular. However, the notorious difficulties of renormalization have made quantum field theory very inaccessible for mathematicians. This provides complete mathematical foundations for the theory of perturbative quantum field theory, based on Wilson's ideas of low-energy effective field theory and on the Batalin-Vilkovisky formalism.
Book Synopsis Lectures On Phase Transitions And The Renormalization Group by : Nigel Goldenfeld
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 417 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.
Book Synopsis Renormalization by : Manfred Salmhofer
Download or read book Renormalization written by Manfred Salmhofer and published by Springer Science & Business Media. This book was released on 2013-03-14 with total page 241 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph is the first to present the recently discovered renormalization techniques for the Schrödinger and Dirac equations, providing a mathematically rigorous, yet simple and clear introduction to the subject. It develops field-theoretic techniques such as Feynman graph expansions and renormalization, taking pains to make all proofs as simple as possible by using generating function techniques throughout. Renormalization is performed by using an exact renormalization group differential equation, a technique that provides simple but complete proofs of the theorems.
Book Synopsis Renormalization by : John C. Collins
Download or read book Renormalization written by John C. Collins and published by Cambridge University Press. This book was released on 2023-07-31 with total page 393 pages. Available in PDF, EPUB and Kindle. Book excerpt:
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 70 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 Scaling and Renormalization in Statistical Physics by : John Cardy
Download or read book Scaling and Renormalization in Statistical Physics written by John Cardy and published by Cambridge University Press. This book was released on 1996-04-26 with total page 264 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text provides a thoroughly modern graduate-level introduction to the theory of critical behaviour. It begins with a brief review of phase transitions in simple systems, then goes on to introduce the core ideas of the renormalisation group.
Book Synopsis Renormalization Group by : Giuseppe Benfatto
Download or read book Renormalization Group written by Giuseppe Benfatto and published by Princeton University Press. This book was released on 1995-07-30 with total page 156 pages. Available in PDF, EPUB and Kindle. Book excerpt: Scaling and self-similarity ideas and methods in theoretical physics have, in the last twenty-five years, coalesced into renormalization-group methods. This book analyzes, from a single perspective, some of the most important applications: the critical-point theory in classical statistical mechanics, the scalar quantum field theories in two and three space-time dimensions, and Tomonaga's theory of the ground state of one-dimensional Fermi systems. The dimension dependence is discussed together with the related existence of anomalies (in Tomonaga's theory and in 4 -e dimensions for the critical point). The theory of Bose condensation at zero temperature in three space dimensions is also considered. Attention is focused on results that can in principle be formally established from a mathematical point of view. The 4 -e dimensions theory, Bose condensation, as well as a few other statements are exceptions to this rule, because no complete treatment is yet available. However, the truly mathematical details are intentionally omitted and only referred to. This is done with the purpose of stressing the unifying conceptual structure rather than the technical differences or subtleties.
Book Synopsis Renormalization by : John Clements Collins
Download or read book Renormalization written by John Clements Collins and published by Cambridge University Press. This book was released on 1984 with total page 396 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a coherent exposition of the techniques underlying these calculations.
Book Synopsis Introduction to Renormalization Group Methods in Physics by : R. J. Creswick
Download or read book Introduction to Renormalization Group Methods in Physics written by R. J. Creswick and published by . This book was released on 2016-06-24 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: This introduction to the renormalization group, an edited and corrected second edition, discusses examples from diverse areas of physics. Designed for a one-semester course for advanced graduate students, the treatment requires a solid background in classical mechanics, statistical mechanics, and quantum mechanics. The text begins with an examination of self-similarity and scale invariance, followed by chapters on the renormalization group approaches to chaos and percolation, renormalization group and critical phenomena, and an extensive treatment of the Ising model. Additional topics include mean field theory and the Gaussian fixed point, the spherical model and the 1/n expansion, the two-dimensional X-Y model and the Kosterlitz-Thouless transition, and other subjects. Each chapter is augmented by problems and references, and three helpful Appendixes supplement the text. AUTHOR: R. J. Creswick is Professor in the Department of Physics and Astronomy, University of South Carolina.
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.
Download or read book Renormalization written by and published by Academic Press. This book was released on 1983-06-23 with total page 203 pages. Available in PDF, EPUB and Kindle. Book excerpt: Renormalization
Book Synopsis Renormalization Methods by : W. D. McComb
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.
Book Synopsis Algebraic Renormalization by : Olivier Piguet
Download or read book Algebraic Renormalization written by Olivier Piguet and published by Springer Science & Business Media. This book was released on 1995-05-17 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.
Book Synopsis Dyson–Schwinger Equations, Renormalization Conditions, and the Hopf Algebra of Perturbative Quantum Field Theory by : Paul-Hermann Balduf
Download or read book Dyson–Schwinger Equations, Renormalization Conditions, and the Hopf Algebra of Perturbative Quantum Field Theory written by Paul-Hermann Balduf and published by Springer Nature. This book was released on with total page 373 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Real-Space Renormalization by : T.W. Burkhardt
Download or read book Real-Space Renormalization written by T.W. Burkhardt and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 226 pages. Available in PDF, EPUB and Kindle. Book excerpt: The renormalization-group approach is largely responsible for the considerable success which has been achieved in the last ten years in developing a complete quantitative theory of phase transitions. Before, there was a useful physical picture of phase transitions, but a general method for making accurate quantitative predictions was lacking. Existent theories, such as the mean-field theory of Landau, sometimes reproduce phase diagrams reliably but were known to fail qualitatively near critical points, where the critical behavior is particularly interesting be cause of its universal character. In the mid 1960's Widom found that the singularities in thermodynamic quanti ties were well described by homogeneous functions. Kadanoff extended the homogeneity hypothesis to correlation functions and linked it to the idea of scale invariance. In the early 1970's Wilson showed how Kadanoff's rescaling could be explicitly carried out near the fixed point of a flow in Hamiltonian space. He made the first practical renormalization-group calculation of the flow induced by the elimination of short-wave-length Fourier components of the order-parameter field. The univer sality of the critical behavior emerges in a natural way in this approach, with a different fixed point for each universality class. The discovery by Wilson and Fisher of a systematic expansion procedure in E for a system in d = 4 - E dimen sions was followed by a cascade of calculations of critical quantities as a function of d and of the order-parameter dimensionality n.
Book Synopsis Introduction to the Functional Renormalization Group by : Peter Kopietz
Download or read book Introduction to the Functional Renormalization Group written by Peter Kopietz and published by Springer. This book was released on 2010-04-22 with total page 380 pages. Available in PDF, EPUB and Kindle. Book excerpt: The renormalization group (RG) has nowadays achieved the status of a meta-theory, which is a theory about theories. The theory of the RG consists of a set of concepts and methods which can be used to understand phenomena in many different ?elds of physics, ranging from quantum ?eld theory over classical statistical mechanics to nonequilibrium phenomena. RG methods are particularly useful to understand phenomena where ?uctuations involving many different length or time scales lead to the emergence of new collective behavior in complex many-body systems. In view of the diversity of ?elds where RG methods have been successfully applied, it is not surprising that a variety of apparently different implementations of the RG idea have been proposed. Unfortunately, this makes it somewhat dif?cult for beginners to learn this technique. For example, the ?eld-theoretical formulation of the RG idea looks at the ?rst sight rather different from the RG approach pioneered by Wilson, the latter being based on the concept of the effective action which is ite- tively calculated by successive elimination of the high-energy degrees of freedom. Moreover, the Wilsonian RG idea has been implemented in many different ways, depending on the particular problem at hand, and there seems to be no canonical way of setting up the RG procedure for a given problem.
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 with total page 424 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).
