Introduction To The Functional Renormalization Group

Author : Peter Kopietz,Lorenz Bartosch,Florian Schütz
Publisher : Springer Science & Business Media
Page : 383 pages
File Size : 52,9 Mb
Release : 2010-05-03
Category : Language Arts & Disciplines
ISBN : 9783642050930

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Introduction to the Functional Renormalization Group by Peter Kopietz,Lorenz Bartosch,Florian Schütz Pdf

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.

Author : Roland Bauerschmidt,David C. Brydges,Gordon Slade
Publisher : Springer Nature
Page : 283 pages
File Size : 53,9 Mb
Release : 2019-10-16
Category : Science
ISBN : 9789813295933

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Introduction to a Renormalisation Group Method by Roland Bauerschmidt,David C. Brydges,Gordon Slade Pdf

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.

Author : Achim Schwenk,Janos Polonyi
Publisher : Springer
Page : 356 pages
File Size : 42,8 Mb
Release : 2012-06-25
Category : Science
ISBN : 9783642273209

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Renormalization Group and Effective Field Theory Approaches to Many-Body Systems by Achim Schwenk,Janos Polonyi Pdf

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.

Author : Martin Reuter,Frank Saueressig
Publisher : Cambridge University Press
Page : 357 pages
File Size : 48,8 Mb
Release : 2019-01-03
Category : Science
ISBN : 9781107107328

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Quantum Gravity and the Functional Renormalization Group by Martin Reuter,Frank Saueressig Pdf

A self-contained pedagogical introduction to asymptotic safety and the functional renormalization group in quantum gravity, for graduate students and researchers.

Author : Martin Reuter,Frank Saueressig
Publisher : Cambridge University Press
Page : 357 pages
File Size : 44,8 Mb
Release : 2019-01-03
Category : Science
ISBN : 9781107107328

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Quantum Gravity and the Functional Renormalization Group by Martin Reuter,Frank Saueressig Pdf

A self-contained pedagogical introduction to asymptotic safety and the functional renormalization group in quantum gravity, for graduate students and researchers.

Author : Manfred Salmhofer
Publisher : Springer Science & Business Media
Page : 241 pages
File Size : 51,7 Mb
Release : 2013-03-14
Category : Science
ISBN : 9783662038734

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Renormalization by Manfred Salmhofer Pdf

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.

Author : Kevin Costello
Publisher : American Mathematical Soc.
Page : 264 pages
File Size : 49,7 Mb
Release : 2011
Category : Mathematics
ISBN : 9780821852880

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Renormalization and Effective Field Theory by Kevin Costello Pdf

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.

Author : Andreas Wipf
Publisher : Springer Nature
Page : 568 pages
File Size : 53,9 Mb
Release : 2021-10-25
Category : Science
ISBN : 9783030832636

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Statistical Approach to Quantum Field Theory by Andreas Wipf Pdf

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.

Author : John Clements Collins
Publisher : Cambridge University Press
Page : 396 pages
File Size : 54,8 Mb
Release : 1984
Category : Science
ISBN : 0521311772

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Renormalization by John Clements Collins Pdf

This book provides a coherent exposition of the techniques underlying these calculations.

Author : John C. Collins
Publisher : Cambridge University Press
Page : 393 pages
File Size : 46,9 Mb
Release : 2023-07-31
Category : Science
ISBN : 9781009401760

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Renormalization by John C. Collins Pdf

Author : Hernan Ocampo,Eddy Pariguan,Sylvie Paycha
Publisher : Cambridge University Press
Page : 435 pages
File Size : 41,9 Mb
Release : 2010-04-29
Category : Science
ISBN : 9781139486736

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Geometric and Topological Methods for Quantum Field Theory by Hernan Ocampo,Eddy Pariguan,Sylvie Paycha Pdf

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.

Author : Nigel Goldenfeld
Publisher : CRC Press
Page : 417 pages
File Size : 44,5 Mb
Release : 2018-03-08
Category : Science
ISBN : 9780429962042

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Lectures On Phase Transitions And The Renormalization Group by Nigel Goldenfeld Pdf

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.

Author : Holt Jeremy W,Kuo Thomas T S,Phua Kok Khoo
Publisher : World Scientific
Page : 536 pages
File Size : 45,6 Mb
Release : 2017-03-27
Category : Science
ISBN : 9789813220676

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Quarks, Nuclei And Stars: Memorial Volume Dedicated For Gerald E Brown by Holt Jeremy W,Kuo Thomas T S,Phua Kok Khoo Pdf

This memorial volume is dedicated to physicist Gerald E Brown (1926–2013) or 'Gerry' as he was known to his many students, postdocs, colleagues and friends. As written by one of the contributors to this book, "Gerry was an inspiring father figure for generations of theoretical nuclear physicists and a great human being". This book covers a wide range of topics in nuclear physics, including nuclear structure, two- and three-body nuclear forces, strangeness nuclear physics, chiral symmetry, hadrons in dense medium, hidden local symmetry, heavy quark symmetry, cosmic neutrinos, nuclear double-beta decay, neutron stars, gravitational waves, renormalization group methods, exotic nuclei, electron ion collider (EIC), and much more. Most of the authors are Gerry's former students and collaborators. We hope readers will find this book very interesting not only for its physics content but also for the window it gives into Gerry's personal legacy and humanity. This book has vivid recollections of Gerry at Stony Brook, Princeton and Copenhagen, together with his humor and his very special intuitive way of thinking.

Author : Timothy J Hollowood
Publisher : Springer Science & Business Media
Page : 78 pages
File Size : 40,7 Mb
Release : 2013-03-28
Category : Science
ISBN : 9783642363122

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Renormalization Group and Fixed Points by Timothy J Hollowood Pdf

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.

Author : Alexander Altland,Ben D. Simons
Publisher : Cambridge University Press
Page : 785 pages
File Size : 40,6 Mb
Release : 2010-03-11
Category : Science
ISBN : 9780521769754

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Condensed Matter Field Theory by Alexander Altland,Ben D. Simons Pdf

This primer is aimed at elevating graduate students of condensed matter theory to a level where they can engage in independent research. Topics covered include second quantisation, path and functional field integration, mean-field theory and collective phenomena.