# Is there a textbook which covers QM via Geometric Algebra (GA)?

There is at least one good book on classical mechanics using Geometric Algebra (GA): New Foundations in Classical Mechanics by David Hestenes.

Likewise there is at least one good book on classical E&M using GA: Understanding Geometric Algebra for Electromagnetic Theory by John W. Arthur.

My question is, is there some analogous book for quantum mechanics? I know, for example, that Pauli matrices can be represented as elements of a Clifford algebra. Is there a textbook that takes this tact? I have seen several short papers on the subject, but no textbook.

• Maybe its your time to write one? Dec 17, 2014 at 2:17
• I was thinking the same thing. Give me a year or two to research and maybe I'll publish one. :) Dec 17, 2014 at 2:20
• what is the advantage of this approach? Dec 17, 2014 at 8:22
• @Jiang-minZhang In my study of GA in the context classical mechanics and E&M, I saw that it $1)$ provided a geometrical intuition to certain scenarios, where otherwise, I'd just be following the math without any picture in my head and $2)$ it sometimes simplifies your algebra (often, though, it really takes just about as long using GA as the standard techniques). Dec 17, 2014 at 17:52
• Also, after spending several months (coming up on a year) studying GA as a mathematical object, I'd like to see exactly where it can go. It can model rotations in classical mechanics and special relativity very succinctly and it's been used to develop an alternative approach to GR. So I'm left to wonder: could we build a solid theory of quantum mechanics on GA? IDK. But I'd like to find out! P.S. To see some of the work that gives me hope, see here. Dec 17, 2014 at 17:58