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Titlebook: Introduction to a Renormalisation Group Method; Roland Bauerschmidt,David C. Brydges,Gordon Slade Book 2019 Springer Nature Singapore Pte

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书目名称Introduction to a Renormalisation Group Method
编辑Roland Bauerschmidt,David C. Brydges,Gordon Slade
视频video
概述Introduces mathematically rigorous renormalisation group theory.Explores mathematically rigorous approaches.Based on the lecture notes for summer school courses
丛书名称Lecture Notes in Mathematics
图书封面Titlebook: Introduction to a Renormalisation Group Method;  Roland Bauerschmidt,David C. Brydges,Gordon Slade Book 2019 Springer Nature Singapore Pte
描述.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 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..
出版日期Book 2019
关键词Gaussian Integration; Gaussian Measures; Ising Model; Perturbative Renormalisation; Phi^4 Spin Model; Ren
版次1
doihttps://doi.org/10.1007/978-981-32-9593-3
isbn_softcover978-981-32-9591-9
isbn_ebook978-981-32-9593-3Series ISSN 0075-8434 Series E-ISSN 1617-9692
issn_series 0075-8434
copyrightSpringer Nature Singapore Pte Ltd. 2019
The information of publication is updating

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The Hierarchical Modelsian free field is a hierarchical field that has comparable large distance behaviour to the lattice Gaussian free field. We explicitly construct a version of the hierarchical Gaussian field and verify that it has the desired properties. We define the hierarchical |.|. model and state the main result
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The Renormalisation Group Maprbative coordinate. The analysis of the renormalisation group map occupies the remainder of the book. An advantage of the hierarchical model is that the analysis can be reduced to individual blocks; this is not the case in the Euclidean setting. We explain this reduction. We discuss progressive inte
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The ,,-Seminormmap. We define the seminorm, prove its important product property, show how it can be used to obtain bounds on derivatives, and explain in which sense the seminorm of a Gaussian expectation is bounded by the expectation of the seminorm. Good properties of the seminorm with respect to exponentiation
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Global Flow: Proof of Theorem 4.2.1rations concerning the typical sizes of the fluctuation and block-spin fields. We state the main estimates on the renormalisation group map in two theorems, and then use these theorems to construct the global renormalisation group flow in the nonperturbative case. The construction requires, in parti
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