Introduction to a Renormalisation Group Method
Authors: Bauerschmidt, Roland, Brydges, David, Slade, Gordon
Free Preview Introduces mathematically rigorous renormalisation group theory
 Explores mathematically rigorous approaches
 Based on the lecture notes for summer school courses
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 About this book

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 φ^{4} models and the selfavoiding walk.
The book begins with critical behaviour and its basic discussion in statistical mechanics models, and subsequently explores perturbative and nonperturbative analysis in the renormalisation group. Lastly it discusses the relation of these topics to the selfavoiding 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.
 About the authors

Roland Bauerschmidt is a University Lecturer in the Department of Pure Mathematics and Mathematical Statistics at the University of Cambridge. His work mainly focuses on the applications of probability theory and analysis to topics in statistical mechanics. He received his Ph.D. in Mathematics from the University of British Columbia in 2013, and was a member of the Institute for Advanced Study in Princeton at the School of Mathematics, and a postdoctoral researcher at Harvard University. He received the IUPAP Young Scientist Prize in 2015.
David C. Brydges is a Professor Emeritus of Mathematics at the University of British Columbia. He works on quantum field theory and statistical mechanics, with an interest in functional integration and probability. He received his Ph.D. from the University of Michigan, and was a Professor at the University of Virginia. He served as the President of the International Association of Mathematics Physics in 20032005, and was elected a Fellow of the Royal Society of Canada in 2007.
Gordon Slade is a Professor in the department of Mathematics at the University of British Columbia. He works on probability theory and statistical mechanics. He received his Ph.D. in Mathematics from the University of British Columbia, and was a Lecturer at the University of Virginia. He was also an Assistant Professor, Associate Professor and Professor at McMaster University. He has been honored with various prizes, e.g., JefferyWilliams Prize, CRMFieldsPIMS Prize, CoxeterJames Prize, and was elected a Fellow of the Royal Society (London), the American Mathematical Society, the Institute of Mathematical Statistics, the Fields Institute and the Royal Society of Canada.
 Table of contents (13 chapters)


Spin Systems
Pages 328

Gaussian Fields
Pages 2936

FiniteRange Decomposition
Pages 3752

The Hierarchical Model
Pages 5365

The Renormalisation Group Map
Pages 6988

Table of contents (13 chapters)
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Bibliographic Information
 Bibliographic Information

 Book Title
 Introduction to a Renormalisation Group Method
 Authors

 Roland Bauerschmidt
 David Brydges
 Gordon Slade
 Series Title
 Lecture Notes in Mathematics
 Series Volume
 2242
 Copyright
 2019
 Publisher
 Springer Singapore
 Copyright Holder
 Springer Nature Singapore Pte Ltd.
 eBook ISBN
 9789813295933
 DOI
 10.1007/9789813295933
 Softcover ISBN
 9789813295919
 Series ISSN
 00758434
 Edition Number
 1
 Number of Pages
 XII, 283
 Number of Illustrations
 15 b/w illustrations, 2 illustrations in colour
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