Introduction to a Renormalisation Group Method PDF Download
Are you looking for read ebook online? Search for your book and save it on your Kindle device, PC, phones or tablets. Download Introduction to a Renormalisation Group Method PDF full book. Access full book title Introduction to a Renormalisation Group Method by Roland Bauerschmidt. Download full books in PDF and EPUB format.
Author: Roland Bauerschmidt
Publisher: Springer Nature
ISBN: 9813295937
Category : Science
Languages : en
Pages : 283
Get Book Here
Book Description
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: Roland Bauerschmidt
Publisher: Springer Nature
ISBN: 9813295937
Category : Science
Languages : en
Pages : 283
Get Book Here
Book Description
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: Richard J. Creswick
Publisher: Wiley-Interscience
ISBN:
Category : Science
Languages : en
Pages : 432
Get Book Here
Book Description
The renormalization group (RG) method has found applications in many areas of physics. The authors present simple RG treatments of such diverse problems as random walks, percolation, chaos and critical phenomena. Detailed introductory materials are presented in each area which makes it reasonably self–contained. The concepts of self–similarity and scale invariance are a common thread tying these problems together. Emphasis is placed on intuitive real–space RG calculations rather than formalism. The momentum–space RG is introduced and the 1/n and epsis expansions are discussed. A brief explanation of the field–theoretic approach to the RG serves as an introduction to more advanced techniques.
Author: Manfred Salmhofer
Publisher: Springer Science & Business Media
ISBN: 3662038730
Category : Science
Languages : en
Pages : 241
Get Book Here
Book Description
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: Peter Kopietz
Publisher:
ISBN: 9783642051371
Category :
Languages : en
Pages : 392
Get Book Here
Book Description
Author: Gérard Toulouse
Publisher: John Wiley & Sons
ISBN:
Category : Mathematics
Languages : en
Pages : 206
Get Book Here
Book Description
Author: J. J. Binney
Publisher: Oxford University Press
ISBN: 0191660566
Category : Science
Languages : en
Pages : 477
Get Book Here
Book Description
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.
Author: W. D. McComb
Publisher: Oxford University Press
ISBN: 0198506945
Category : Business & Economics
Languages : en
Pages : 349
Get Book Here
Book Description
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.
Author: John Cardy
Publisher: Cambridge University Press
ISBN: 9780521499590
Category : Science
Languages : en
Pages : 264
Get Book Here
Book Description
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.
Author: P.J. Grout
Publisher: Springer Science & Business Media
ISBN: 1402087071
Category : Science
Languages : en
Pages : 586
Get Book Here
Book Description
In this volume we have collected some of the contributions made to the Twelfth European Workshop on Quantum Systems in Chemistry and Physics (QSCP-XII) in 2007. The workshop was held at Royal Holloway College, the most westerly campusof the University of London,and situated just a stone’s throw from Windsor Great Park. The workshop, which ran from 30 August to 5 September, continued the series that was established by Roy McWeeny in April 1996 with a meeting held at San Miniato, near Pisa. The purpose of the QSCP workshops is to bring together, in an informal atmosphere and with the aim of fostering collaboration, those chemists and physicists who share a common ?eld of interest in the theory of the quantum many-body problem. Quantum mechanics provides a theoretical foundation for our understandingof the structure,propertiesanddynamicsof atoms, moleculesandthe solid state, in terms of their component particles: electrons and nuclei. The study of ‘Quantum Systems in Chemistry and Physics’ therefore underpins many of the emerging?elds in twenty-?rstcenturyscience andtechnology:nanostructure,smart materials, drug design – to name but a few. Members of the workshop were keen to discuss their research and engage in collaboration centred upon the development of fundamental and innovative theory which would lead to the exploration of new concepts. The proceedings of all of the workshops, which have been held annually since 1996, have been published both to disseminate the latest developments within the wider community and to stimulate further collaboration.
Author: Peter Kopietz
Publisher: Springer Science & Business Media
ISBN: 364205093X
Category : Language Arts & Disciplines
Languages : en
Pages : 383
Get Book Here
Book Description
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.
