Modern Geometric Structures And Fields pdf epub mobi txt 電子書下載 2024

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I.S. Novikov

American Mathematical Society

2006

633

USD 81.00

Hardcover

Graduate Studies in Mathematics

9780821839294

圖書標籤: 數學幾何物理數學物理微分幾何7 geometry Structures Modern

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发表于2024-05-10

Modern Geometric Structures And Fields epub 下載 mobi 下載 pdf 下載 txt 電子書下載 2024

Modern Geometric Structures And Fields pdf epub mobi txt 電子書下載 2024

圖書描述

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.

Modern Geometric Structures And Fields 下載 mobi epub pdf txt 電子書

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Modern Geometric Structures And Fields pdf epub mobi txt 電子書下載

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是《現代幾何俄羅斯譯叢》的凝聚版本。楊米爾斯方程建立在帶聯絡的主縴維叢上的理論。聯絡在縴維叢引入微分結構。切叢聯絡相容與度量産生瞭鏇量場。縴維叢幾何與規範場物理的翻譯詞典：連接函數就是規範變換；聯絡1-形式是規範場勢（證明通過水平提升）是主叢外的新結構，麯率2-形式是規範場強，麯率要滿足恒等式；物質場是伴矢量從的截麵，協變導數是物質場和規範場的作用，kibble方程的分類。狹義相對論和廣義相對論區分在於廣義相對論的度規張量（引力就是度規張量）不平凡，廣義相對論是彎麯的，狄拉剋方程的基礎建立在剋勞福德代數基礎上：SO(1,3)的半自鏇錶示和SL(2,C)的標準錶示相同，SL(2,C)的李代數和洛倫茨群同構，狄拉剋方程式是自鏇場，當質量為0描述光子時候，就是不相關的兩個外爾方程。

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典型俄羅斯教材-科普的手法將專業知識

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典型俄羅斯教材-科普的手法將專業知識

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