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Geometrical formulation of renormali...

Kikuchi, Yuta.

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Geometrical formulation of renormalization-group method as an asymptotic analysis = with applications to derivation of causal fluid dynamics /

Record Type:	Electronic resources : Monograph/item
Title/Author:	Geometrical formulation of renormalization-group method as an asymptotic analysis/ by Teiji Kunihiro, Yuta Kikuchi, Kyosuke Tsumura.
Reminder of title:	with applications to derivation of causal fluid dynamics /
Author:	Kunihiro, Teji.
other author:	Kikuchi, Yuta.
Published:	Singapore :Springer Singapore : : 2022.,
Description:	xvii, 486 p. :ill., digital ;24 cm.
[NT 15003449]:	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 Kuramoto's 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.
Contained By:	Springer Nature eBook
Subject:	Renormalization group. -
Online resource:	https://doi.org/10.1007/978-981-16-8189-9
ISBN:	9789811681899

Geometrical formulation of renormalization-group method as an asymptotic analysis = with applications to derivation of causal fluid dynamics /
Kunihiro, Teji.

Geometrical formulation of renormalization-group method as an asymptotic analysiswith applications to derivation of causal fluid dynamics /[electronic resource] :by Teiji Kunihiro, Yuta Kikuchi, Kyosuke Tsumura. - Singapore :Springer Singapore :2022. - xvii, 486 p. :ill., digital ;24 cm. - Fundamental theories of physics,v. 2062365-6425 ;. - Fundamental theories of physics ;v. 206..

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 Kuramoto's 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.

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.

ISBN: 9789811681899

Standard No.: 10.1007/978-981-16-8189-9doiSubjects--Topical Terms:

736411
Renormalization group.

LC Class. No.: QC20.7.R43 / K85 2022

Dewey Class. No.: 530.143

Geometrical formulation of renormalization-group method as an asymptotic analysis = with applications to derivation of causal fluid dynamics /
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505 0 $a 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 Kuramoto's 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.
520 $a 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.
650 0 $a Renormalization group. $3 736411
650 1 4 $a Mathematical Methods in Physics. $3 890898
650 2 4 $a Theoretical, Mathematical and Computational Physics. $3 1066859
650 2 4 $a Mathematical Physics. $3 1542352
650 2 4 $a Nonlinear Optics. $3 3538901
700 1 $a Kikuchi, Yuta. $3 3596660
700 1 $a Tsumura, Kyosuke. $3 3596661
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773 0 $t Springer Nature eBook
830 0 $a Fundamental theories of physics ; $v v. 206. $3 3596662
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950 $a Physics and Astronomy (SpringerNature-11651)