作者：(伊朗)阿里·索贾-法尔德
页数：186
出版社：哈尔滨工业大学出版社
出版日期：2022
ISBN：9787576702781
电子书格式：pdf/epub/txt
内容简介
本书是一部英文版的涉及理论物理的数学专著。本著作重点研究了Hopf代数扰动重正化在量子场论研究中的一些近期新应用.在第一部分中，我们介绍了可积重正化形式主义，作为研究基于Feynman图的Hopf代数的可积系统的一种方法.此外，我们考虑了一种可以替代量子可积系统的方法，该方法与重正化Hof代数的无穷维复李群紧密相关.在第二部分中，我们考虑了将Connes-Marcolli的通用方法扩展到非扰动量子场论研究的过程中。
作者简介
阿里·索贾-法尔德，伊朗人，在沙希德·贝赫什提大学获得博士学位。他曾在豪斯道夫数学学院，马克思·普朗克数学学院和欧文·薛定谔国际数学实验物理学院做访问学者，并在攻读博士学位期间完成了研究工作。
目录
1 Introduction
2 Hopf Algebra Structures on Combinatorial Objects
2.1 Elementary properties
2.2 Combinatorial Hopf algebras
2.2.1 Connes-Kreimer Hopf algebra
2.2.2 Rooted trees and (quasi-)symmetric functions
2.2.3 Incidence Hopf algebras
3 Perturbative Renormalization
3.1 Insertion operator: From a pre-Lie algebra structure on Feynman diagrams to a Hopf algebra
3.2 Hopf algebraic formalism
4 Integrable Renormalization
4.1 Integrable systems: from finite dimension (geometric approach) to infinite dimen-sion (algebraic approach)
4.2 Rota-Baxter type algebras
4.3 Theory of quantum integrable systems
4.4 Integrable systems on the basis of the renormalization group
4.5 Baditoiu-Rosenberg framework: The continuation of the standard process
4.6 Fixed point equations
5 Connes-Marcolli Theory
5.1 Geometric nature of counterterms: Category of flat equi-singular connections
5.2 The construction of a universal Tannakian category
6 Universal Hopf Algebra of Renormalization
6.1 Shuffle type representation.
6.2 Rooted tree type representation
6.3 Universal counterterms
7 Combinatorial Dyson-Schwinger Equations and Connes-Marcolli Universal Treat-ment
7.1 Quantum motions in terms of the renormalization Hopf algebra
7.2 Universal Hopf algebra of renormalization and factorization problem
7.3 DSEs in a categorical framework
8 From Combinatorial Dyson-Schwinger Equations to the Category of Feynman Motivic Sheaves
8.1 DSEs in the context of the theory of motives
9 Conclusion
编辑手记
2 Hopf Algebra Structures on Combinatorial Objects
2.1 Elementary properties
2.2 Combinatorial Hopf algebras
2.2.1 Connes-Kreimer Hopf algebra
2.2.2 Rooted trees and (quasi-)symmetric functions
2.2.3 Incidence Hopf algebras
3 Perturbative Renormalization
3.1 Insertion operator: From a pre-Lie algebra structure on Feynman diagrams to a Hopf algebra
3.2 Hopf algebraic formalism
4 Integrable Renormalization
4.1 Integrable systems: from finite dimension (geometric approach) to infinite dimen-sion (algebraic approach)
4.2 Rota-Baxter type algebras
4.3 Theory of quantum integrable systems
4.4 Integrable systems on the basis of the renormalization group
4.5 Baditoiu-Rosenberg framework: The continuation of the standard process
4.6 Fixed point equations
5 Connes-Marcolli Theory
5.1 Geometric nature of counterterms: Category of flat equi-singular connections
5.2 The construction of a universal Tannakian category
6 Universal Hopf Algebra of Renormalization
6.1 Shuffle type representation.
6.2 Rooted tree type representation
6.3 Universal counterterms
7 Combinatorial Dyson-Schwinger Equations and Connes-Marcolli Universal Treat-ment
7.1 Quantum motions in terms of the renormalization Hopf algebra
7.2 Universal Hopf algebra of renormalization and factorization problem
7.3 DSEs in a categorical framework
8 From Combinatorial Dyson-Schwinger Equations to the Category of Feynman Motivic Sheaves
8.1 DSEs in the context of the theory of motives
9 Conclusion
编辑手记
