物理学家用的微分几何和李群

出版时间：2008-11  出版社：世界图书出版公司  作者：斯洛伐 费茨科  页数：697  
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前言

　　This is an introductory text dealing with a part of mathematics： modem differential geometry and the theory of Lie groups. It is written from the perspective of and mainly for the needs of physicists. The orientation on physics makes itself felt in the choice of material， in the way it is presented （e.g. with no use of a definition-theorem-proof scheme）， as well as in the content of exercises （often they are closely related to physics）.　　Its potential readership does not， however， consist of physicists alone. Since the book is about mathematics， and since physics has served for a fairly long time as a rich source of inspiration for mathematics， it might be useful for the mathematical community as well. More generally， it is suitable for anybody who has some （rather modest） preliminary background knowledge （to be specified in a while） and who desires to become familiar in a comprehensible way with this interesting， important and living subject， which penetrates increasingly into various branches of modem theoretical physics， "pure" mathematics itself， as well as into its numerous applications.

内容概要

　微分几何在现代理论物理和应用数学中扮演着越来越重要的角色。本书给出了在理论物理和应用数学中很重要的几何知识的引入，包括，流形、张量场、微分形式、联络、辛几何、李群作用、族以及自旋。　本书以一种非正式的形式写作，作者给出了1000多例子重在强调对一般理论的深刻理解。本书将要为读者很好的学习拉格郎日现代处理方法、哈密顿力学、电磁、规范场，相对论以及万有引力做充足的准备。　本书很适合作为物理、数学以及工程专业的高年级本科生以及研究生的教程，也是一本很难得自学教程。　

书籍目录

PrefaceIntroduction1　The　concept　of　a　manifold2　Vector　and　tensor　fields3　Mappings　of　tensors　induced　by　mappings　of　manifolds4　Lie　derivative5　Exterior　algebra6　Differential　calulus　of　forms7　Integral　calculus　of　forms8　Particular　cases　and　applications　of　Stokes'theorem9　Poincare　lemma　and　cohomologies10　Lie　groups:basic　facts11　Differential　geometry　on　Lie　groups12　Representations　of　Lie　groups　and　Lie　algebras13　Actions　of　Lie　groups　and　Lie　algebras　on　manifolds14　Hamiltonian　mechanics　and　symplectic　manifolds15　Parallel　transport　and　linear　connection　on　M16　Field　theory　and　the　language　of　forms17　Differential　geometry　on　T　M　and　T*M18　Hamiltonian　and　Lagrangian　equations19　Linear　connection　and　the　frame　bundle20　Connection　on　a　principal　G-bundle21　Gauge　theories　and　connections22　Spinor　fields　and　the　Dirac　operatorAppendix　A　Some　relevant　algebrai　structuresAppendix　B　Starring

用户评论 (总计3条)

•   书是从物理初学者角度写的，所以和初学者相适应，不过想提高可以再配合另外的微分几何一起看，甚至可以是数学系用的教材
•   适合学物理的看，就是印刷质量不好
•   这个内容很多，看完需要花很多时间