物理学家用的几何代数

Hacker News 上怎么说

• jacobolus · 2016 年

  ……你如果对李群理论（Lie theory）或表示论（representation theory）感兴趣，可以看看这篇论文[《Lie Groups as Spin Groups》][lgasg]。如果你是物理学者 / 物理系学生 / 电气工程师等，可以试试[《Geometric Algebra for Physicists》][gap]，或者[《Understanding Geometric Algebra for Electromagnetic Theory》][gaet]。如果想换个稍微不同的视角，不妨看看 [Sobczyk][] 的[《New Foundations in Mathematics: The Geometric Concept……

  …you’re interested in Lie theory or representation theory, check out this paper [“Lie Groups as Spin Groups”][lgasg]. If you’re a physicist / physics student / electrical engineer / etc., try the book [Geometric Algebra for Physicists][gap] or perhaps [Understanding Geometric Algebra for Electromagnetic Theory][gaet] For a slightly different perspective, take a look at [Sobczyk][]’s [New Foundations in Mathematics: The Geometric Concept…

• happy4crazy · 2011 年

  如果你喜欢摆弄四元数（quaternions），那几何代数（geometric algebra）可能也会让你觉得很有趣。《Geometric Algebra for Physicists》讲得非常清晰，节奏也很平缓。http://www.amazon.com/Geometric-Algebra-Physicists-Chris-Dor... 这一本看起来也很棒：http://www.amazon.com/Linear-Geometric-Algebra-Alan-Macdonal...

  If you enjoy playing around with quaternions, you may also have fun with geometric algebra. Geometric Algebra for Physicists is very clear and gently paced. http://www.amazon.com/Geometric-Algebra-Physicists-Chris-Dor... This one also looks good: http://www.amazon.com/Linear-Geometric-Algebra-Alan-Macdonal...

• eigenspace · 2018 年

  张量代数（Tensor algebra）完全可以用几何代数来表达。如果你感兴趣，我推荐 Doran 和 Lasenby 写的《Geometric Algebra for Physicists》。

  Tensor algebra is fully expressible in terms of geometric algebra. If you're itnerested, I'd reccomend Geometric Algebra for Physicists by Doran and Lasenby.

• eigenspace · 2019 年

  ……在我心里一直给几何代数（Geometric Algebra）留着位置，但我认为在它真正得到广泛应用之前，符号表示上还需要很多改进。如果你对 GA 的现状感到好奇，我建议看看 Doran 和 Lasenby 写的《Geometric Algebra for Physicists》。

  …in my heart from Geometric Algebra, but I think it still needs a lot of notational improvement before it'll ever see any real adoption. If you're curious about GA as it currently stands, I'd check out Geometric Algebra for Physicists by Doran and Lasenby.

• jordibc · 2023 年

  ……书之外，我还想提两本让我大开眼界且整体非常赞的冷门佳作：* Mahajan 写的《Street-Fighting Mathematics》（http://streetfightingmath.com/）。直观、实用且有趣。* Doran 和 Lasenby 写的《Geometric Algebra for Physicists》。我发现几何代数的威力和优雅令人着迷，哪怕这本书也涉及物理，而且可能还有更合适的纯数学几何代数书籍，……

  …books, I also wanted to mention two outliers that I found eye-opening and generally awesome: * Street-Fighting Mathematics, by Mahajan (http://streetfightingmath.com/). Intuitive, useful and fun. * Geometric Algebra for Physicists, by Doran and Lasenby. I found the power and elegance of geometric algebra mesmerizing, and even if this book is also about physics and there may be more appropriate math-only books about geometric algebra,…

• dorchadas · 2023 年

  > * Doran 和 Lasenby 写的《Geometric Algebra for Physicists》。我发现几何代数的威力和优雅令人着迷，哪怕这本书也涉及物理，而且可能还有更合适的纯数学几何代数书籍，……

  > * Geometric Algebra for Physicists, by Doran and Lasenby. I found the power and elegance of geometric algebra mesmerizing, and even if this book is also about physics and there may be more appropriate math-only books about geometric algebra,…

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