Name: Geometric Algebra for Physicists
ISBN: 9780521715959

Geometric Algebra for Physicists

Geometric algebra is a powerful mathematical language with applications across a range of subjects in physics and engineering. This book is a complete guide to the current state of the subject with early chapters providing a self-contained introduction to geometric algebra. Topics covered include new techniques for handling rotations in arbitrary dimensions, and the links between rotations, bivectors and the structure of the Lie groups. Following chapters extend the concept of a complex analytic function theory to arbitrary dimensions, with applications in quantum theory and electromagnetism. Later chapters cover advanced topics such as non-Euclidean geometry, quantum entanglement, and gauge theories. Applications such as black holes and cosmic strings are also explored. It can be used as a graduate text for courses on the physical applications of geometric algebra and is also suitable for researchers working in the fields of relativity and quantum theory.

What Hacker News says

hamish_toddJun 2026

If you want to learn physics from a geometric viewpoint, GA is brilliant. Here's a playlist of my stuff, which is aimed at computer graphics folks: https://youtube.com/playlist?list=PL9a8DfUJQcuA9AXqvjxYolq5-...

Leading up to classical mechanics, you have the 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.

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ColinHayhurstNov 2024

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

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fouricAug 2024

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 as rigorous, as I would like. I should try to re-read with Eric's criticisms in mind.

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adrian_bAug 2023

For studying geometric algebras, it should help a lot if one is already familiar with abstract algebraic structures, like groups, rings, fields, linear spaces a.k.a. vector spaces.

I have not found yet any book that I consider really satisfactory, mainly because all of them are more or less incomplete, which is understandable, because a 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, which had previously remained a niche domain of mathematics for about a century after the too early death of their discoverer, William Kingdon Clifford.

There are also many more recent books, which can be seen e.g. through a search on Amazon or other such sites, but I have not searched such books during the last years, so I do not know which of them are good.

The older books are good enough to provide an understanding of geometric algebras, but for practical applications one usually must go beyond them.

Even without applying in practice the theory of geometric algebras, it is still useful to understand it, because this removes most of the mystery from mathematical physics and it allows a more efficient organization in your head of the knowledge about it.

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jordibcJan 2023

For sure I got significantly(?) better with classics like Spivak, Apostol, Rudin.

"Real and Complex Analysis" by Rudin, and the two books both named "Calculus" from Spivak and Apostol. But also from Apostol his more concise and far-reaching "Mathematical Analysis". And from Spivak his small gem "Calculus On Manifolds" made quite a dent on me.

Other than more "classic math" 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, this is the one that made it for me.

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dorchadasJan 2023

> * 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, this is the one that made it for me.

I've tried to read several of them, and, sadly, I feel most geometric algebra books fail at explaining it. It's a shame as it's part of what kindled my interest in pure mathematics and I still feel I'm nowhere nearer understanding it despite working through several other mathematics textbooks, including just plain algebra. But, it did spark my interest and now I've moved on to other interesting topics, though Geometric Algebra is still my white whale.

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