國立高雄大學圖資館 |

登入

回首頁

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

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Geometrical formulation of renormalization-group method as an asymptotic analysisby Teiji Kunihiro, Yuta Kikuchi, Kyosuke Tsumura.
其他題名:	with applications to derivation of causal fluid dynamics /
作者:	Kunihiro, Teji.
其他作者:	Kikuchi, Yuta.
出版者:	Singapore :Springer Singapore :2022.
面頁冊數:	xvii, 486 p. :ill., digital ;24 cm.
Contained By:	Springer Nature eBook
標題:	Renormalization group.
電子資源:	https://doi.org/10.1007/978-981-16-8189-9
ISBN:	9789811681899$q(electronic bk.)

Geometrical formulation of renormalization-group method as an asymptotic analysiswith 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.172..

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$q(electronic bk.)

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

266976
Renormalization group.

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

Dewey Class. No.: 530.143

Geometrical formulation of renormalization-group method as an asymptotic analysiswith applications to derivation of causal fluid dynamics /
LDR:03819nmm a2200337 a 4500 001 623355
003 DE-He213
005 20220401200458.0
006 m d
007 cr nn 008maaau
008 221209s2022 si s 0 eng d
020 $a 9789811681899$q(electronic bk.)
020 $a 9789811681882$q(paper)
024 7 $a 10.1007/978-981-16-8189-9 $2 doi
035 $a 978-981-16-8189-9
040 $a GP $c GP
041 0 $a eng
050 4 $a QC20.7.R43 $b K85 2022
072 7 $a PHU $2 bicssc
072 7 $a SCI040000 $2 bisacsh
072 7 $a PHU $2 thema
082 0 4 $a 530.143 $2 23
090 $a QC20.7.R43 $b K96 2022
100 1 $a Kunihiro, Teji. $3 925510
245 1 0 $a Geometrical formulation of renormalization-group method as an asymptotic analysis $h [electronic resource] : $b with applications to derivation of causal fluid dynamics / $c by Teiji Kunihiro, Yuta Kikuchi, Kyosuke Tsumura.
260 $a Singapore : $b Springer Singapore : $b Imprint: Springer, $c 2022.
300 $a xvii, 486 p. : $b ill., digital ; $c 24 cm.
490 1 $a Fundamental theories of physics, $x 2365-6425 ; $v v. 206
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 266976
650 1 4 $a Mathematical Methods in Physics. $3 273796
650 2 4 $a Theoretical, Mathematical and Computational Physics. $3 376743
650 2 4 $a Mathematical Physics. $3 522725
650 2 4 $a Nonlinear Optics. $3 913464
700 1 $a Kikuchi, Yuta. $3 925511
700 1 $a Tsumura, Kyosuke. $3 925512
710 2 $a SpringerLink (Online service) $3 273601
773 0 $t Springer Nature eBook
830 0 $a Fundamental theories of physics ; $v v.172. $3 563650
856 4 0 $u https://doi.org/10.1007/978-981-16-8189-9
950 $a Physics and Astronomy (SpringerNature-11651)