分析、流形和物理学
全新正版 极速发货
￥ 79.64 5.7折 ￥ 139 全新
库存4件
广东广州
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作者(法)肖凯-布吕埃(Yvonne Choquet-Bruhat) 著 著 著
出版社世界图书出版公司
ISBN9787510084423
出版时间2015-01
装帧平装
开本16开
定价139元
货号1201073845
上书时间2024-12-18
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目录
Preface to the second edition
Preface
Contents
Conventions
I. REVIEW OF FUNDAMENTAL NOTIONS OF ANALYSIS
1.Graded algebras
2.Berezinian
3.Tensor product of algebras
4.Clifford algebras
5.Clifford algebra as a coset of the tensor algebra
6.Fierz identity
7.Pin and Spin groups
8.Weyl spinors, helicity operator; Majorana pinors, charge
conjugation
9.Representations of Spin(n, m), n+m odd
10.Dirac adjoint
11.Lie algebra of Pin(n, m) and Spin(n, m)
12.Compact spaces
13.Compactness in weak star topology
14.Homotopy groups, general properties
15.Homotopy of topological groups
16.Spectrum of closed and self-adjoint linear operators
II. DIFFERENTIAL CALCULUS ON BANACH SPACES
1.Supersmooth mappings
2.Berezin integration; Gaussian integrals
3.Noethers theorems I
4.Noethers theorems II
5.Invarianceof the equations of motion
6.String action
7.Stress-energy tensor; energy with respect to a timelike vector field
III. DIFFERENTIABLE MANIFOLDS
1.Sheaves
2.Differentiable submanifolds
3.Subgroups of Lie groups. When are they Lie subgroups?
4.Cartan-Killing form on the Lie algebra g of a Lie group G
5.Direct and semidirect products of Lie groups and their Lie algebra
6.Homomorphisms and antihomomorphisms of a Lie algebra into
spaces of vector fields
7.Homogeneous spaces; symmetric spaces
8.Examples of homogeneous spaces, Stiefel and Grassmann manifolds
9.Abelian representations of nonabelian groups
10.Irreducibility and reducibility
11.Characters
12.Solvable Lie groups
13.Lie algebras of linear groups
14.Graded bundles
IV. INTEGRATION ON MANIFOLDS
1.Cohomology. Definitions and exercises
2.Obstruction to the construction of Spin and Pin bundles;
Stiefel-Whitney classes
3.Inequivalent spin structures
4.Cohomology of groups
5.Lifting a group action
6.Short exact sequence; Weyl Heisenberg group
……
内容摘要
本书分为2卷,第1卷1977年初版，之后7次重印或修订。第2卷也在原来的基础上做了不少改进，增加了一部分内容讲述主纤维丛上的连通，包括完整，协变倒数，曲率，线性连通，示性类和不变曲率积分。书中有部分内容完全重写，增加了不少例子和练习，使得内容更加容易理解。目次：分析基本观点；Banach空间上的微积分；微分流行、有限维的例子；流形上的积分；Riemannian流形，K?hlerian流形；分布；微分流形，无限维的例子。读者对象：适用于物理、数学专业研究人员和学生。
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