Roland Bauerschmidt - Introduction to a Renormalisation Group Method (Lecture Notes in Mathematics (2242))

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This book provides an introduction to a mathematically rigorous renormalisation group method which is inspired by Kenneth Wilsons original ideas from the early 1970s, for which he was awarded the 1982 Nobel Prize in Physics. The method has been developed and applied over the past 10 years in a series of papers authored by various subsets of the present authors, along with Martin Lohmann, Alexandre Tomberg and Benjamin Wallace.

We present the general setting of the problems in critical phenomena that have been addressed by the method, with focus on the 4-dimensional | | 4 spin system and the 4-dimensional continuous-time weakly self-avoiding walk. We give a self-contained analysis of the 4-dimensional hierarchical | | 4 model, which is simpler than its Euclidean counterpart but still reveals many of the ideas and techniques of the renormalisation group method. We comment on, and give detailed references for, the extension of the method to the Euclidean setting in Chap.. The book is intended to be a starting point for a reader who may not have prior knowledge of the renormalisation group method.

We are grateful to Manfred Salmhofer and Christoph Kopper in Heidelberg; to Stefan Adams in Warwick; to Kyeong-Hun Kim, Panki Kim and Hyunjae Yoo in Daejeon; to Damien Calaque and Dominique Manchon in Montpellier; to Michele Corregi, Alessandro Giuliani, Vieri Mastropietro and Alessandro Pizzo in Rome; and to Stefan Adams, Jean-Bernard Bru and Walter de Siqueira Pedra in Bilbao for organising these events and for the invitations to lecture.

We are especially grateful to Alexandre Tomberg who gave tutorials for our courses in Heidelberg and Daejeon and to Benjamin Wallace who gave tutorials in Bilbao. Each has contributed in several ways during the early stages of the writing of this book.

This work was supported in part by NSERC of Canada, by the US NSF under agreement DMS-1128155 and by the Simons Foundation.