可读性较高的一本书

这本好书一直没有书评，小弟我就抛砖引玉吧。 昨天从卓越入手的，今天读到第三章。书的字体和纸张有点像小说。行文娓娓道来，解释清晰明了。由于作者的用意在于引导，而不是完整严格地处理全部内容，所以详略非常合像我这种偏物理不好纯数学的读者的胃口，没有必要繁复证明地地方简略说明或者留作习题。图示和习题安排都恰到好处。可读性强，但也并不是易读——书中通过形象的方式介绍完抽象的概念不会详细解读其例子和应用，而是常常留作习题，所以需要脑补的地方还是蛮多的，而且很多地方处理有点sloppy（随意），所以看的时候还是有本正式的Text在旁参考比较好，书中有推荐，这里就不敷述了。 目录贴一下： 第一部分 Electromagnetism: Maxwell's Equations Manifolds Vector Fields Differential Forms Rewriting Maxwell's Equations DeRham Theory in Electromagnetism 第二部分 Gauge Fields: Symmetry Bundles and Connections Curvature and the Yang-Mills Equation Chern-Simons Theory Link Invariants from Gauge Theory 第三部分 Gravity: Semi-Riemannian Geometry Einstein's Equation Lagrangians for General Relativity The ADM Formalism The New Variables 大家可以到http://www.worldscibooks.com/physics/2324.html 看更详细的介绍。 有位老兄写了篇很不错的英文评论，发下链接： http://complementaryslackness.wordpress.com/2009/02/01/book-review-gauge-fields-knots-and-gravity/ 最主要他还把一二部分的习题全部做了。这本书一个让人着急的地方就是正常课本开始讲例题的时候，它开始顺手布置下习题。。。汗。所以有了题解是大贡献。 题解在此：http://www.iap.tu-darmstadt.de/tqp/grp_jrenes/gfkg.html 我这里贴一下序中对全书的简要介绍： The book is divided into three parts that treat electromagnetism, gauge theory, and general relativity, respectively. Part I of this book introduces the language of modern differential geometry, and shows how Maxwell's equations can be drastically simplified using this lan- guage. We stress the coordinate-free approach and the relevance of global topological considerations in understanding such things as the Bohm-Aharonov effect, wormholes, and magnetic monopoles. Part II introduces the mathematics of gauge theory -- fiber bundles, connec- tions and curvature -- and then introduces the Yang-Mills equation, Chern classes, and Chern-Simons classes. It also includes a brief intro- duction to knot theory and its relation to Chern-Simons theory. Part III introduces the basic concepts of Riemannian and semi-Riemannian geometry and then concentrates on topics in general relativity of spe- cial importance to quantum gravity: the Einstein-Hilbert and Palatini formulations of the action principle for gravity, the ADM formalism, and canonical quantization. Here we emphasize tensor computations written in the notation used in general relativity. We conclude this part with a sketch of Ashtekar's 'new variables' and the way Chern-Simons theory provides a solution to the Wheeler-DeWitt equation (the basic equation of canonical quantum gravity). 另外这里还有一个不错的帖子，问题提得好，回答更妙，所以很有参考价值： http://www.physicsforums.com/showthread.php?t=255736 嗯，抛砖引玉就到这吧。我是受可读性这一个特性吸引而买的，感觉很值得。更适合该领域的初学者。 将持续更新读书笔记： 第一部分： http://book.douban.com/annotation/12348303/