Modern Geometric Structures And Fields 在线电子书 pdf 下载 txt下载 epub 下载 mobi 下载 2024

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I.S. Novikov 作者

American Mathematical Society

译者

2006 出版日期

633 页数

USD 81.00 价格

Hardcover

Graduate Studies in Mathematics 丛书系列

9780821839294 图书编码

Modern Geometric Structures And Fields 在线电子书图书标签: 数学几何物理数学物理微分几何7 geometry Structures Modern

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Modern Geometric Structures And Fields 在线电子书 epub 下载 mobi 下载 pdf 下载 txt 下载 2024

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是《现代几何俄罗斯译丛》的凝聚版本。杨米尔斯方程建立在带联络的主纤维丛上的理论。联络在纤维丛引入微分结构。切丛联络相容与度量产生了旋量场。纤维丛几何与规范场物理的翻译词典：连接函数就是规范变换；联络1-形式是规范场势（证明通过水平提升）是主丛外的新结构，曲率2-形式是规范场强，曲率要满足恒等式；物质场是伴矢量从的截面，协变导数是物质场和规范场的作用，kibble方程的分类。狭义相对论和广义相对论区分在于广义相对论的度规张量（引力就是度规张量）不平凡，广义相对论是弯曲的，狄拉克方程的基础建立在克劳福德代数基础上：SO(1,3)的半自旋表示和SL(2,C)的标准表示相同，SL(2,C)的李代数和洛伦茨群同构，狄拉克方程式是自旋场，当质量为0描述光子时候，就是不相关的两个外尔方程。

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The book presents the basics of Riemannian geometry in its modern form as geometry of differentiable manifolds and the most important structures on them. The authors' approach is that the source of all constructions in Riemannian geometry is a manifold that allows one to compute scalar products of tangent vectors. With this approach, the authors show that Riemannian geometry has a great influence to several fundamental areas of modern mathematics and its applications. In particular, Geometry is a bridge between pure mathematics and natural sciences, first of all physics. Fundamental laws of nature are formulated as relations between geometric fields describing various physical quantities. The study of global properties of geometric objects leads to the far-reaching development of topology, including topology and geometry of fiber bundles. Geometric theory of Hamiltonian systems, which describe many physical phenomena, led to the development of symplectic and Poisson geometry. Field theory and the multidimensional calculus of variations, presented in the book, unify mathematics with theoretical physics. Geometry of complex and algebraic manifolds unifies Riemannian geometry with modern complex analysis, as well as with algebra and number theory. Prerequisites for using the book include several basic undergraduate courses, such as advanced calculus, linear algebra, ordinary differential equations, and elements of topology.

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