Geometrical formulation of renormalization-group method as an asymptotic analysis : with applications to derivation of causal fluid dynamic / Teiji Kunihiro, Yuta Kikuchi, Kyosuke Tsumura.
Kunihiro, Teiji, author.; Kikuchi, Yuta, author.; Tsumura, Kyosuke, author.
2022
QC20.7.R43
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Title
Geometrical formulation of renormalization-group method as an asymptotic analysis : with applications to derivation of causal fluid dynamic / Teiji Kunihiro, Yuta Kikuchi, Kyosuke Tsumura.
Author
Kunihiro, Teiji, author.
ISBN
9789811681899 (electronic bk.)
9811681899 (electronic bk.)
9789811681882 (print)
9811681880
DOI
https://doi.org/10.1007/978-981-16-8189-9
Published
Singapore : Springer, 2022.
Language
English
Description
1 online resource (1 volume) : illustrations (black and white, and color).
Item Number
10.1007/978-981-16-8189-9 doi
Call Number
QC20.7.R43
Dewey Decimal Classification
530.14/3
Summary
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.
Bibliography, etc. Note
Includes bibliographical references and index.
Access Note
Access limited to authorized users.
Source of Description
Description based on print version record.
Added Author
Kikuchi, Yuta, author.
Tsumura, Kyosuke, author.
Series
Fundamental theories of physics ; v. 206.
Available in Other Form
GEOMETRICAL FORMULATION OF RENORMALIZATION-GROUP METHOD AS AN ASYMPTOTIC ANALYSIS.
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Notion of Effective Theories in Physical Sciences
Divergence and Secular Term in the Perturbation Series of Ordinary Differential Equations
Traditional Resummation Methods
Elementary Introduction of the RG method in Terms of the Notion of Envelopes
Ei-Fujii-Kunihiro Formulation and Relation to Kuramotos reduction scheme
Relation to the RG Theory in Quantum Field Theory
Resummation of the Perturbation Series in Quantum Methods
Illustrative Examples
Slow Dynamics Around Critical Point in Bifurcation Phenomena
Dynamical Reduction of A Generic Non-linear Evolution Equation with Semi-simple Linear Operator
A Generic Case when the Linear Operator Has a Jordan-cell Structure
Dynamical Reduction of Difference Equations
Slow Dynamics in Some Partial Differential Equations
Some Mathematical Formulae
Dynamical Reduction of Kinetic Equations
Relativistic First-Order Fluid Dynamic Equation
Doublet Scheme and its Applications
Relativistic Causal Fluid dynamic Equation
Numerical Analysis of Transport Coefficients and Relaxation Times
Reactive Multi-component Systems
Non-relativistic Case and Application to Cold Atoms
Summary and Future Prospects.

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