物理学的几何
The Geometry of Physics
Theodore Frankel · 初版 1997 年
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“本书旨在提供有关 exterior differential forms、differential geometry、algebraic and differential topology、Lie groups、vector bundles 以及 Chern forms 的实用知识，这些对于深入理解经典与现代 physics 及 engineering 至关重要。书中涵盖了 analytical and fluid dynamics、electromagnetism（在平坦和弯曲空间中）、thermodynamics、elasticity 的 deformation tensors、soap films、special and general relativity、Dirac operator 与 spinors，以及包括 Yang-Mills、Aharonov-Bohm ef 在内的 gauge fields 的讨论
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……能更有帮助。既然李代数（Lie algebras）是微分流形的特殊类型，你通过学习几何能搞懂不少东西，而且这很快会引向规范场论（gauge theory）和现代物理学。西奥多·弗兰克尔（Theodore Frankel）写的《物理学的几何学：导论》（The Geometry of Physics: An Introduction）在阐释几何学的许多方面做得很好，甚至为一些经典物理学提供了几何直觉。对于广义……
…to be more helpful. Since Lie algebras are special types of differential manifolds, you can learn quite a bit by studying the geometry and this quickly leads into gauge theory and modern physics. The Geometry of Physics: An Introduction, by Theodore Frankel does a good job illustrating a lot of aspects of geometry even offering some geometric insight into some classical physics. It is an absolute necessity for general…
西奥多·弗兰克尔的《物理学的几何学：导论》（The Geometry of Physics: An Introduction）：一部将你在物理学中学到的那些全凭直觉比划手势（hand-wavy）的内容完全形式化的杰作。会彻底改变你的认知视角。赫伯特（Herbert）的《热力学与恒温统计导论》（Thermodynamics and an Introduction to Thermostatistics）……
The Geometry of Physics: An Introduction by Theodore Frankel A masterpiece that formalizes all of the handway bits you learned in physics. Will change your perspective forever. Thermodynamics and an Introduction to Thermostatistics Herbert…
在过去的一年里，我从头到尾精读了弗兰克尔的《物理学的几何学》（The Geometry of Physics），倒不是为了重学物理，而是为了重新构建一套在物理中实际使用的现代几何工具箱：流形、微分形式、联络与曲率、李群与李代数（Lie groups and algebras）、纤维……
Over the past year I worked through Frankel’s “The Geometry of Physics” cover to cover, not to relearn physics, but to rebuild a modern geometric toolbox as it is actually used there: manifolds, differential forms, connections and curvature, Lie groups and algebras, fiber…