Renormalization Theory
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Renormalization
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Author : Laurie M. Brown
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Renormalization written by Laurie M. Brown and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Science categories.
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.
Renormalization Group
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Author : Giuseppe Benfatto
language : en
Publisher: Princeton University Press
Release Date : 2020-11-10
Renormalization Group written by Giuseppe Benfatto and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-11-10 with Science categories.
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.
The Theory Of Critical Phenomena
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Author : J. J. Binney
language : en
Publisher: Oxford University Press
Release Date : 1992-06-11
The Theory Of Critical Phenomena written by J. J. Binney and has been published by Oxford University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1992-06-11 with Science categories.
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.
Renormalization Group And Fixed Points
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Author : Timothy J Hollowood
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-28
Renormalization Group And Fixed Points written by Timothy J Hollowood and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-28 with Science categories.
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.
Field Theory The Renormalization Group And Critical Phenomena Graphs To Computers 3rd Edition
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Author : Daniel J Amit
language : en
Publisher: World Scientific Publishing Company
Release Date : 2005-06-21
Field Theory The Renormalization Group And Critical Phenomena Graphs To Computers 3rd Edition written by Daniel J Amit and has been published by World Scientific Publishing Company this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-06-21 with Science categories.
This volume links field theory methods and concepts from particle physics with those in critical phenomena and statistical mechanics, the development starting from the latter point of view. Rigor and lengthy proofs are trimmed by using the phenomenological framework of graphs, power counting, etc., and field theoretic methods with emphasis on renormalization group techniques. Non-perturbative methods and numerical simulations are introduced in this new edition. Abundant references to research literature complement this matter-of-fact approach. The book introduces quantum field theory to those already grounded in the concepts of statistical mechanics and advanced quantum theory, with sufficient exercises in each chapter for use as a textbook in a one-semester graduate course.The following new chapters are included:I. Real Space MethodsII. Finite Size ScalingIII. Monte Carlo Methods. Numerical Field Theory
Renormalization
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Author : John C. Collins
language : en
Publisher: Cambridge University Press
Release Date : 2023-07-31
Renormalization written by John C. Collins and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-07-31 with Science categories.
Renormalization
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Author : John Clements Collins
language : en
Publisher: Cambridge University Press
Release Date : 1984
Renormalization written by John Clements Collins and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1984 with Science categories.
This book provides a coherent exposition of the techniques underlying these calculations.
Renormalization Theory
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Author : G.P Velo
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Renormalization Theory written by G.P Velo and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Science categories.
The present volume collects lecture notes from the session of the International School of Mathematical Physics 'Ettore Majorana' on Renormalization Theory that took place in Erice (Sicily), August 17 to August 31, 1975. The School was a NATO Advanced Study Institute sponsored by the Italian Ministry of Public Education, the Italian Minis try of Scientific and Technological Research, and the Regional Sicilian Government. Renormalization theory has, by now, acquired forty years of history. The present volume assumes a general acquaintance with the elementary facts of the subject as they might appear in an introductory course in quantum field theory. For more recent significant developments it provides a systematic intro duction as well as a detailed discussion of the existing state of knowledge. In particular analytic and dimensional renorma lization, normal product technique, and the Bogoliubov-Shirkov Epstein-Glaser method are treated, with applications to physically important gauge theories. All the preceding deals with perturbative renormalization theory. In recent years there has been an interesting development of non-perturbative renormalization theory in models in space-times of two and three dimensions, with the use of the methods of constructive field theory. Despite the simplicity of these models, the results are of significance because they are exact and answer a number of questions of principle. There are parts of renormalization theory which are not well understood, for instance the renormalization theory of non-renormalizable interactions.
Renormalization And Effective Field Theory
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Author : Kevin Costello
language : en
Publisher: American Mathematical Society
Release Date : 2022-04-25
Renormalization And Effective Field Theory written by Kevin Costello and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-04-25 with Mathematics categories.
This book tells mathematicians about an amazing subject invented by physicists and it tells physicists how a master mathematician must proceed in order to understand it. Physicists who know quantum field theory can learn the powerful methodology of mathematical structure, while mathematicians can position themselves to use the magical ideas of quantum field theory in “mathematics” itself. The retelling of the tale mathematically by Kevin Costello is a beautiful tour de force. —Dennis Sullivan This book is quite a remarkable contribution. It should make perturbative quantum field theory accessible to mathematicians. There is a lot of insight in the way the author uses the renormalization group and effective field theory to analyze perturbative renormalization; this may serve as a springboard to a wider use of those topics, hopefully to an eventual nonperturbative understanding. —Edward Witten 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 book 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. As an example, a cohomological proof of perturbative renormalizability of Yang–Mills theory is presented. An effort has been made to make the book accessible to mathematicians who have had no prior exposure to quantum field theory. Graduate students who have taken classes in basic functional analysis and homological algebra should be able to read this book.
Algebraic Renormalization
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Author : Olivier Piguet
language : en
Publisher: Springer Science & Business Media
Release Date : 2008-09-11
Algebraic Renormalization written by Olivier Piguet and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-09-11 with Science categories.
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.