镜对称简介
发布时间：2019-03-26 11:55
【摘要】：本文是一篇介绍数学物理中镜对称的综述类文章.镜对称最初于1990年左右从弦论中提出,之后便引起了物理学家和数学家的关注,除了物理学家对其的应用外,数学家对猜想本身的具体刻画与证明产生了浓厚兴趣,并发展了代数和几何两大类研究方法,取得了不少进展.如今,镜对称已成为联系理论物理,辛几何,代数几何的最主要的交叉领域,也是数学物理中最富生机的领域之一.本文从多个方面对镜对称进行介绍,以给读者对其初步的了解:第一章,介绍镜对称的概况和发展历史,和相关学习资料.第二章,简短介绍物理中sigma模型和其中一个镜对称的例子.第三章,介绍1994年由Maxim Kontsevich建立使用代数方法的的同调镜对称[K],它对镜对称数学方面的早期研究有很大的影响.第四章,简短介绍1996年的由Strominger-Yau-Zaslow建立的用使用几何方法的SYZ镜对称[SYZ],并给出T-对偶的一个例子.第五章,介绍同调镜对称中Fakaya范畴所属的A∞-范畴的基本概念.第六章,介绍根据同调镜对称发展出的带角辛流形的基本概念.
[Abstract]:This paper is an overview of mirror symmetry in mathematical physics. Mirror symmetry was first proposed from string theory in about 1990, and then aroused the attention of physicists and mathematicians. In addition to physicists' application to it, mathematicians were interested in the concrete characterization and proof of conjecture itself. Two kinds of research methods, algebra and geometry, have been developed, and a lot of progress has been made. Nowadays mirror symmetry has become one of the most dynamic fields in mathematical physics as well as the main cross-fields of theoretical physics symplectic geometry and algebraic geometry. This paper introduces mirror symmetry from many aspects in order to give readers a preliminary understanding of it. Chapter one introduces the general situation and development history of mirror symmetry and related learning materials. In the second chapter, we briefly introduce the sigma model in physics and an example of mirror symmetry. In the third chapter, we introduce the homotopy symmetry [K] which was established by Maxim Kontsevich in 1994 using algebraic method, which has a great influence on the early study of mirror symmetry mathematics. In chapter 4, we briefly introduce the SYZ mirror symmetry with geometric method [SYZ], which was established by Strominger-Yau-Zaslow in 1996, and give an example of T-duality. In chapter 5, we introduce the basic concept of A 鈭，
本文编号：2447520
[Abstract]:This paper is an overview of mirror symmetry in mathematical physics. Mirror symmetry was first proposed from string theory in about 1990, and then aroused the attention of physicists and mathematicians. In addition to physicists' application to it, mathematicians were interested in the concrete characterization and proof of conjecture itself. Two kinds of research methods, algebra and geometry, have been developed, and a lot of progress has been made. Nowadays mirror symmetry has become one of the most dynamic fields in mathematical physics as well as the main cross-fields of theoretical physics symplectic geometry and algebraic geometry. This paper introduces mirror symmetry from many aspects in order to give readers a preliminary understanding of it. Chapter one introduces the general situation and development history of mirror symmetry and related learning materials. In the second chapter, we briefly introduce the sigma model in physics and an example of mirror symmetry. In the third chapter, we introduce the homotopy symmetry [K] which was established by Maxim Kontsevich in 1994 using algebraic method, which has a great influence on the early study of mirror symmetry mathematics. In chapter 4, we briefly introduce the SYZ mirror symmetry with geometric method [SYZ], which was established by Strominger-Yau-Zaslow in 1996, and give an example of T-duality. In chapter 5, we introduce the basic concept of A 鈭，
本文编号：2447520
本文链接：https://www.wllwen.com/shoufeilunwen/benkebiyelunwen/2447520.html
