Geometric Algebra for Physicists
by Anthony Lasenby · first published 2003
80% recommend20% neutral
Why HN recommends it
Clear, gently paced introduction to geometric algebra for physicists, covering a wide range of physics topics such as electrodynamics. Suited to students as well as working physicists and engineers.
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…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…
on “Clifford Algebra: A visual introduction (2014)” ↗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...
on “Even Great Mathematicians Guess Wrong” ↗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.
on “Let's remove Quaternions from every 3D Engine” ↗…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.
on “How Feynman Diagrams Revolutionized Physics” ↗…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,…
on “Ask HN: Math books that made you significantly better at math?” ↗> * 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,…
on “Ask HN: Math books that made you significantly better at math?” ↗…complete presentation would require a huge amount of work for rewriting the manuals for all the branches of traditional physics to use models based on geometric algebras. An older decent introduction is "Geometric Algebra for Physicists" by Chris Doran and Anthony Lasenby. There are also several older books, which need more mathematical experience, by David Hestenes, who was responsible for the revival of the theory of geometric algebras,…
on “A Swift intro to Geometric Algebra” ↗I'm currently very slowly making my way through Geometric Algebra for Physicists by Doran and Lasenby. The book is a delight to read, but I'm not a mathematician, and this article is showing me that my small amount of understanding is...not nearly as deep, and especially not nearly…
on “Poor Foundations in Geometric Algebra” ↗Complex numbers and (Pauli/Dirac) matrices not required if you use Geometric Algebra. I highly recommend the book by Doran and Lasenby [0], or you can get the details from their papers, notably [1]. [0] Geometric Algebra for Physicists, CUP, 2003 [1] https://arxiv.org/abs/quant-ph/0509178
on “January 1928: Dirac equation unifies quantum mechanics and special relativity” ↗…simpler to express when the fields are grouped logically into a single entity. A great reference that explores electrodynamics and many other geometric algebra physics topics is Doran and Lasenby's "Geometric Algebra for Physicists" ( https://www.cambridge.org/core/books/geometric-algebra-for-p... ). Be warned that the reference above is a tough read. I have a for dummies exploration of some of the electromagnetism applications…
on “Ganja.js: Geometric Algebra Generator for JavaScript, C++, C#, Rust, Python” ↗David Hestenes’s Geometric Algebra for Physicists, maybe?
on “What is the inverse of a vector?” ↗I'm currently going through Geometric Algebra for Physicists, and find it exceedingly clear: https://g.co/kgs/ciKXVS
on “Introduction to Clifford Algebra (2006)” ↗In case it helps: In addition to "Geometric Algebra for Physicists" (whose first two chapters I'd recommend to get a nice overview), I found Hestenes' "New Foundations for Classical Mechanics" to be very good and readable. Also, there are many good resources in https://bivector.net/…
on “Ask HN: Math books that made you significantly better at math?” ↗…sibgraphi tutorials: https://youtube.com/playlist?list=PLsSPBzvBkYjxrsTOr0KLDilkZ... (I also recommend the bivector discord if you want a community) And from there, sudgy's videos are good, and the tome "geometric algebra for physicists" packs in a huge amount of stuff.
on “The case against geometric algebra” ↗Geometric Algebra for Physicists : https://www.amazon.com/Geometric-Algebra-Physicists-Chris-Do...
on “BiVector.net – Geometric Algebra for CGI, Vision and Engineering” ↗