Introduction To The Functional Renormalization Group
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Introduction To The Functional Renormalization Group
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Author : Peter Kopietz
language : en
Publisher: Springer
Release Date : 2010-04-22
Introduction To The Functional Renormalization Group written by Peter Kopietz and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-04-22 with Science categories.
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.
Introduction To The Functional Renormalization Group
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Author : Peter Kopietz
language : en
Publisher: Springer Science & Business Media
Release Date : 2010-05-03
Introduction To The Functional Renormalization Group written by Peter Kopietz 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 2010-05-03 with Language Arts & Disciplines categories.
This book, based on a graduate course given by the authors, is a pedagogic and self-contained introduction to the renormalization group with special emphasis on the functional renormalization group. The functional renormalization group is a modern formulation of the Wilsonian renormalization group in terms of formally exact functional differential equations for generating functionals. In Part I the reader is introduced to the basic concepts of the renormalization group idea, requiring only basic knowledge of equilibrium statistical mechanics. More advanced methods, such as diagrammatic perturbation theory, are introduced step by step. Part II then gives a self-contained introduction to the functional renormalization group. After a careful definition of various types of generating functionals, the renormalization group flow equations for these functionals are derived. This procedure is shown to encompass the traditional method of the mode elimination steps of the Wilsonian renormalization group procedure. Then, approximate solutions of these flow equations using expansions in powers of irreducible vertices or in powers of derivatives are given. Finally, in Part III the exact hierarchy of functional renormalization group flow equations for the irreducible vertices is used to study various aspects of non-relativistic fermions, including the so-called BCS-BEC crossover, thereby making the link to contemporary research topics.
Introduction To A Renormalisation Group Method
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Author : Roland Bauerschmidt
language : en
Publisher: Springer Nature
Release Date : 2019-10-16
Introduction To A Renormalisation Group Method written by Roland Bauerschmidt and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-10-16 with Science categories.
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.
Quantum Gravity And The Functional Renormalization Group
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Author : Martin Reuter
language : en
Publisher: Cambridge University Press
Release Date : 2019-01-03
Quantum Gravity And The Functional Renormalization Group written by Martin Reuter 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 2019-01-03 with Science categories.
A self-contained pedagogical introduction to asymptotic safety and the functional renormalization group in quantum gravity, for graduate students and researchers.
Renormalization Group And Effective Field Theory Approaches To Many Body Systems
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Author : Achim Schwenk
language : en
Publisher: Springer
Release Date : 2012-06-28
Renormalization Group And Effective Field Theory Approaches To Many Body Systems written by Achim Schwenk and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-06-28 with Science categories.
There have been many recent and important developments based on effective field theory and the renormalization group in atomic, condensed matter, nuclear and high-energy physics. These powerful and versatile methods provide novel approaches to study complex and strongly interacting many-body systems in a controlled manner. The six extensive lectures gathered in this volume combine selected introductory and interdisciplinary presentations focused on recent applications of effective field theory and the renormalization group to many-body problems in such diverse fields as BEC, DFT, extreme matter, Fermi-liquid theory and gauge theories. Primarily aimed at graduate students and junior researchers, they offer an opportunity to explore fundamental physics across subfield boundaries at an early stage in their careers.
Statistical Approach To Quantum Field Theory
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Author : Andreas Wipf
language : en
Publisher: Springer Nature
Release Date : 2021-10-25
Statistical Approach To Quantum Field Theory written by Andreas Wipf and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-10-25 with Science categories.
This new expanded second edition has been totally revised and corrected. The reader finds two complete new chapters. One covers the exact solution of the finite temperature Schwinger model with periodic boundary conditions. This simple model supports instanton solutions – similarly as QCD – and allows for a detailed discussion of topological sectors in gauge theories, the anomaly-induced breaking of chiral symmetry and the intriguing role of fermionic zero modes. The other new chapter is devoted to interacting fermions at finite fermion density and finite temperature. Such low-dimensional models are used to describe long-energy properties of Dirac-type materials in condensed matter physics. The large-N solutions of the Gross-Neveu, Nambu-Jona-Lasinio and Thirring models are presented in great detail, where N denotes the number of fermion flavors. Towards the end of the book corrections to the large-N solution and simulation results of a finite number of fermion flavors are presented. Further problems are added at the end of each chapter in order to guide the reader to a deeper understanding of the presented topics. This book is meant for advanced students and young researchers who want to acquire the necessary tools and experience to produce research results in the statistical approach to Quantum Field Theory.
Handbook Of Quantum Gravity
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Author : Cosimo Bambi
language : en
Publisher: Springer Nature
Release Date : 2024-12-03
Handbook Of Quantum Gravity written by Cosimo Bambi and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-12-03 with Science categories.
The search for a theory of quantum gravity is one of the most important and fascinating problems in modern theoretical physics. While we do not have yet a complete theory of quantum gravity, significant advancements have been done in the past decades. In this handbook, every section is dedicated to a specific approach towards a theory of quantum gravity and is edited by the leading experts in the field. This book represents both a valuable resource for graduate students and an important reference for researchers in quantum gravity.
Geometric And Topological Methods For Quantum Field Theory
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Author : Hernan Ocampo
language : en
Publisher: Cambridge University Press
Release Date : 2010-04-29
Geometric And Topological Methods For Quantum Field Theory written by Hernan Ocampo 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 2010-04-29 with Science categories.
Aimed at graduate students in physics and mathematics, this book provides an introduction to recent developments in several active topics at the interface between algebra, geometry, topology and quantum field theory. The first part of the book begins with an account of important results in geometric topology. It investigates the differential equation aspects of quantum cohomology, before moving on to noncommutative geometry. This is followed by a further exploration of quantum field theory and gauge theory, describing AdS/CFT correspondence, and the functional renormalization group approach to quantum gravity. The second part covers a wide spectrum of topics on the borderline of mathematics and physics, ranging from orbifolds to quantum indistinguishability and involving a manifold of mathematical tools borrowed from geometry, algebra and analysis. Each chapter presents introductory material before moving on to more advanced results. The chapters are self-contained and can be read independently of the rest.
Origin Of Mass And Strong Coupling Gauge Theories Scgt 15 Proceedings Of The Sakata Memorial Kmi Workshop
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Author : Yasumichi Aoki
language : en
Publisher: World Scientific
Release Date : 2017-12-06
Origin Of Mass And Strong Coupling Gauge Theories Scgt 15 Proceedings Of The Sakata Memorial Kmi Workshop written by Yasumichi Aoki and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-12-06 with Science categories.
This volume contains contributions to the workshop, which was largely focused on the strong coupling gauge theories in search for theories beyond the standard model, particularly, the LHC experiments and lattice studies of conformal fixed point. The main topics include walking technicolor and the role of conformality in view of the 125 GeV Higgs as a light composite Higgs (technidilaton, and other composite Higgs, etc.). Nonperturbative studies like lattice simulations and stringy/holographic approaches are extensively discussed in close relation to the phenomenological studies.After the discovery of 125 GeV Higgs at LHC, the central issue of particle physics is now to reveal the dynamical origin of the Higgs itself. One of the possibilities would be the composite Higgs based on the strong coupling gauge theory in the TeV region, such as the technidilaton predicted in walking technicolor with infrared conformality. The volume contains, among others, many of the latest important reports on walking technicolor and related subjects in the general context of conformality, in a way of direct relevance to the LHC phenomenology as well as the lattice studies. It is very timely to study full theoretical implications in the exciting era when the LHC is vigorously working. This volume is of great importance for that purpose.Speakers of 40 talks (plus posters) include K-I Aoki, Y Aoki, K Bamba, E Bennett, R S Chivukula, H Georgi, A Hasenfratz, D-K Hong, K Itoh, D Elander, G Fleming, H Fukano, Y Iwasaki, M Jarvinen, D Kadoh, S Kim, R Kitano, K-I Kondo, J Kuti, D Lin, N Maru, H Matsufuru, S Matsuzaki, K-I Nagai, C Nonaka, H Ohki, E Pallante, M Rho, E Rinaldi, F Sannino, D Schaich, A Shibata, R E Shrock, E H Simmons, K Tuominen, C H Wong, N Yamada, M J S Yang, and K Yamawaki.
Renormalization
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Author : Manfred Salmhofer
language : en
Publisher: Springer
Release Date : 2010-12-01
Renormalization written by Manfred Salmhofer and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-12-01 with Science categories.
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.