東華大學圖書館 |

Language: English

Help

回圖書館首頁

手機版館藏查詢

Back

Switch To: Labeled | MARC Mode | ISBD

Linked to FindBook

Google Book

Amazon

博客來

Dyson-Schwinger equations, renormalization conditions, and the hopf algebra of perturbative quantum field theory

Record Type:	Electronic resources : Monograph/item
Title/Author:	Dyson-Schwinger equations, renormalization conditions, and the hopf algebra of perturbative quantum field theory/ by Paul-Hermann Balduf.
Author:	Balduf, Paul-Hermann.
Published:	Cham :Springer Nature Switzerland : : 2024.,
Description:	xvi, 363 p. :ill. (some col.), digital ;24 cm.
Notes:	"Doctoral thesis accepted by Humboldt University of Berlin, Germany."
[NT 15003449]:	Introduction to perturbative quantum field theory -- Hopf algebra theory of renormalization -- Renormalized Green functions in kinematic renormalization -- Renormalization group and Dyson-Schwinger equations in non-kinematic renormalization -- Field diffeomorphisms and symmetries -- Conclusion and outlook.
Contained By:	Springer Nature eBook
Subject:	Renormalization (Physics) -
Online resource:	https://doi.org/10.1007/978-3-031-54446-0
ISBN:	9783031544460

Dyson-Schwinger equations, renormalization conditions, and the hopf algebra of perturbative quantum field theory
Balduf, Paul-Hermann.

Dyson-Schwinger equations, renormalization conditions, and the hopf algebra of perturbative quantum field theory[electronic resource] /by Paul-Hermann Balduf. - Cham :Springer Nature Switzerland :2024. - xvi, 363 p. :ill. (some col.), digital ;24 cm. - Springer theses,2190-5061. - Springer theses..

"Doctoral thesis accepted by Humboldt University of Berlin, Germany."

Introduction to perturbative quantum field theory -- Hopf algebra theory of renormalization -- Renormalized Green functions in kinematic renormalization -- Renormalization group and Dyson-Schwinger equations in non-kinematic renormalization -- Field diffeomorphisms and symmetries -- Conclusion and outlook.

This book offers a systematic introduction to the Hopf algebra theory of renormalization in quantum field theory. Special emphasis is put on physical motivation for mathematical constructions, the role of Dyson-Schwinger equations (DSEs), renormalization conditions, and the renormalization group. The bulk of the book deals with the similarities and differences between two popular renormalization conditions, kinematic renormalization (MOM) and Minimal Subtraction (MS) MOM is a physical global boundary condition for Green functions. DSEs can then be solved in terms of power series which only involve finite renormalized quantities. Conversely, MS is defined order-by-order based on divergences of the unrenormalized Green function. We show that MS is equivalent to MOM with coupling-dependent renormalization point. We determine the large-order growth of series coefficients in different renormalization schemes and derive a novel analytic formula for the all-order solution of linear DSEs in MS. Finally, we derive the changes in off-shell Green functions and counterterms under nonlinear redefinition of field variables for self-interacting scalar fields. The book is aimed at mathematically oriented physicists and physically interested mathematicians who seek a systematic overview of the Hopf algebra theory of renormalization and DSEs.

ISBN: 9783031544460

Standard No.: 10.1007/978-3-031-54446-0doiSubjects--Topical Terms:

661787
Renormalization (Physics)

LC Class. No.: QC174.17.R46

Dewey Class. No.: 530.143

Dyson-Schwinger equations, renormalization conditions, and the hopf algebra of perturbative quantum field theory
LDR:02835nmm a22003495a 4500 001 2370803
003 DE-He213
005 20240427130409.0
006 m d
007 cr nn 008maaau
008 241127s2024 sz s 0 eng d
020 $a 9783031544460 $q (electronic bk.)
020 $a 9783031544453 $q (paper)
024 7 $a 10.1007/978-3-031-54446-0 $2 doi
035 $a 978-3-031-54446-0
040 $a GP $c GP
041 0 $a eng
050 4 $a QC174.17.R46
072 7 $a PHP $2 bicssc
072 7 $a SCI057000 $2 bisacsh
072 7 $a PHP $2 thema
082 0 4 $a 530.143 $2 23
090 $a QC174.17.R46 $b B179 2024
100 1 $a Balduf, Paul-Hermann. $3 3716384
245 1 0 $a Dyson-Schwinger equations, renormalization conditions, and the hopf algebra of perturbative quantum field theory $h [electronic resource] / $c by Paul-Hermann Balduf.
260 $a Cham : $b Springer Nature Switzerland : $b Imprint: Springer, $c 2024.
300 $a xvi, 363 p. : $b ill. (some col.), digital ; $c 24 cm.
490 1 $a Springer theses, $x 2190-5061
500 $a "Doctoral thesis accepted by Humboldt University of Berlin, Germany."
505 0 $a Introduction to perturbative quantum field theory -- Hopf algebra theory of renormalization -- Renormalized Green functions in kinematic renormalization -- Renormalization group and Dyson-Schwinger equations in non-kinematic renormalization -- Field diffeomorphisms and symmetries -- Conclusion and outlook.
520 $a This book offers a systematic introduction to the Hopf algebra theory of renormalization in quantum field theory. Special emphasis is put on physical motivation for mathematical constructions, the role of Dyson-Schwinger equations (DSEs), renormalization conditions, and the renormalization group. The bulk of the book deals with the similarities and differences between two popular renormalization conditions, kinematic renormalization (MOM) and Minimal Subtraction (MS) MOM is a physical global boundary condition for Green functions. DSEs can then be solved in terms of power series which only involve finite renormalized quantities. Conversely, MS is defined order-by-order based on divergences of the unrenormalized Green function. We show that MS is equivalent to MOM with coupling-dependent renormalization point. We determine the large-order growth of series coefficients in different renormalization schemes and derive a novel analytic formula for the all-order solution of linear DSEs in MS. Finally, we derive the changes in off-shell Green functions and counterterms under nonlinear redefinition of field variables for self-interacting scalar fields. The book is aimed at mathematically oriented physicists and physically interested mathematicians who seek a systematic overview of the Hopf algebra theory of renormalization and DSEs.
650 0 $a Renormalization (Physics) $3 661787
650 0 $a Quantum field theory. $3 523766
650 1 4 $a Elementary Particles, Quantum Field Theory. $3 894026
650 2 4 $a Mathematical Physics. $3 1542352
710 2 $a SpringerLink (Online service) $3 836513
773 0 $t Springer Nature eBook
830 0 $a Springer theses. $3 1314442
856 4 0 $u https://doi.org/10.1007/978-3-031-54446-0
950 $a Physics and Astronomy (SpringerNature-11651)