Geometrical Formulation of Renormalization-Group Method as an Asymptotic Analysis: With Applications to Derivation of Causal Fluid Dynamics (1st ed. 2022) (Fundamental Theories of Physics #206)

By: Teiji Kunihiro and Yuta Kikuchi and Kyosuke Tsumura

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Synopsis: This book presents a comprehensive account of the renormalization-group (RG) method and its extension, the doublet scheme, in a geometrical point of view. It extract long timescale macroscopic/mesoscopic dynamics from microscopic equations in an intuitively understandable way rather than in a mathematically rigorous manner and introduces readers to a mathematically elementary, but useful and widely applicable technique for analyzing asymptotic solutions in mathematical models of nature. The book begins with the basic notion of the RG theory, including its connection with the separation of scales. Then it formulates the RG method as a construction method of envelopes of the naive perturbative solutions containing secular terms, and then demonstrates the formulation in various types of evolution equations. Lastly, it describes successful physical examples, such as stochastic and transport phenomena including second-order relativistic as well as nonrelativistic fluid dynamics with causality and transport phenomena in cold atoms, with extensive numerical expositions of transport coefficients and relaxation times. Requiring only an undergraduate-level understanding of physics and mathematics, the book clearly describes the notions and mathematical techniques with a wealth of examples. It is a unique and can be enlightening resource for readers who feel mystified by renormalization theory in quantum field theory.

Book Quality:: Publisher Quality
ISBN-13:: 9789811681899
Related ISBNs:: 9789811681882
Publisher:: Springer Singapore, Singapore
Date of Addition:: 05/03/22
Copyrighted By:: Springer Nature Singapore Pte Ltd.
Adult content:: No
Language:: English
Has Image Descriptions:: No
Categories:: Nonfiction, Science, Earth Sciences, Mathematics and Statistics
Submitted By:: Bookshare Staff
Usage Restrictions:: This is a copyrighted book.