Introduction to a Renormalisation Group Method
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Beschreibung
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.
These lectures provides a brief introduction to the theory of critical phenomena, including the Ising and φ4 spin models, and the strictly and weakly self-avoiding walk. Then recent results in dimension 4 for the φ4 model and the weakly self-avoiding walk are discussed. These results have been obtained using a rigorous renormalisation group method. Several tools that are fundamental to the renormalisation group method are subsequently introduced, including Gaussian integration, perturbative renormalisation, and the stable manifold theorem. The last third of these lectures discusses non-perturbative aspects of the implementation of a renormalisation group step. Tutorials are included.
Introduces mathematically rigorous renormalisation group theory Explores mathematically rigorous approaches Based on the lecture notes for summer school courses
Autor*in
Roland Bauerschmidt
Themen in »Introduction to a Renormalisation Group Method«
Gaussian Integration Gaussian Measures Ising Model Perturbative Renormalisation Phi^4 Spin Model Renormalisation Group Method Scaling Limits Self-avoiding Walk Stable Manifold Theorem Theory of Critical Phenomena