Geometrical Formulation of Renormalization-Group Method as an Asymptotic Analysis
With Applications to Derivation of Causal Fluid Dynamics
Buch in deiner Nähe kaufen
Beschreibung
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.
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.
Sheds light on geometrical notion of renormalization group theory Offers systematic asymptotic analysis in evolution equations Describes contents a priori and clearly
Autor*in
Teiji Kunihiro
Themen in »Geometrical Formulation of Renormalization-Group Method as an Asymptotic Analysis«
Renormalization Group Theory in Differential Equations Asymptotic Analysis of Differential Equations Krylov-Bogoliubov-Mitropolsky Theory Kuramoto's Formulation of Generalized Reduction Theory Ei-Fujii-Kunihiro Formulation The Doublet Scheme Fluid Dynamic Limits of Boltzmann Equation Causal Relativistic Fluid Dynamic Equations