Geometrical Formulation of Renormalization-Group Method as an Asymptotic Analysis: With Applications to Derivation of Causal Fluid Dynamics

The renormalization-group (RG) method and its extension, the doublet scheme, are presented in this book in a geometrical point of view. It extracts long timescale macroscopic/mesoscopic dynamics from microscopic equations in an intuitively understandable way, introducing readers to a mathematically elementary technique for analyzing asymptotic solutions in mathematical models of nature. Examples include stochastic and transport phenomena, with extensive numerical expositions of transport coefficients and relaxation times.

Format: Hardback
Length: 486 pages
Publication date: 02 April 2022
Publisher: Springer Verlag, Singapore

This comprehensive book delves into the realm of the renormalization-group (RG) method and its extension, the doublet scheme, from a geometrical perspective. It offers a unique approach to extracting long-timescale macroscopic/mesoscopic dynamics from microscopic equations, making them intuitively understandable rather than solely relying on rigorous mathematical techniques. By introducing readers to a mathematically elementary yet highly useful and widely applicable technique for analyzing asymptotic solutions in mathematical models of nature, the book aims to bridge the gap between theory and application.

The book begins by exploring the fundamental concept of the RG theory, including its connection with the separation of scales. It then proceeds to formulate the RG method as a construction method of envelopes for naive perturbative solutions that encompass secular terms. This formulation is demonstrated across various types of evolution equations, showcasing its versatility.

Furthermore, the book provides successful physical examples, encompassing stochastic and transport phenomena, including second-order relativistic as well as nonrelativistic fluid dynamics with causality, as well as transport phenomena in cold atoms, with extensive numerical expositions of transport coefficients and relaxation times. The text assumes only an undergraduate-level understanding of physics and mathematics, ensuring that the notions and mathematical techniques are clearly explained with a wealth of examples.

This book stands out as a unique and enlightening resource for readers who may feel overwhelmed by renormalization theory in quantum field theory. Its comprehensive coverage and intuitive approach make it an invaluable tool for those seeking to deepen their understanding of this complex subject.

Weight: 916g
Dimension: 235 x 155 (mm)
ISBN-13: 9789811681882
Edition number: 1st ed. 2022