Talk:Geometric algebra
Not that I have anything against Hestenes-worshippers (I met Hestenes once and he's a nice guy, if a little bit ..... well, let me put it this way: I think he said Clifford algebras will settle all questions of physics, or something like that) .... OK, where was I? Oh: Well doesn't Emil Artin also warrant some attention on this page? -- Mike Hardy
I've never heard of a geometric algebra before, but your remark about Grassmann algebras giving a more natural treatment of physics without complex numbers piqued my interest, although I don't quite see how. Would you care to clarify what you meant? Phys 17:33, 20 Aug 2003 (UTC)
- Hmm, I just read a bit of it, but I still don't see anything new geometric algebra has to say that can't be said already in the language of differential geometry and "dot products", linear representations, etc.. Phys 10:31, 21 Aug 2003 (UTC)
- Also, I'm a bit suspicious of defining the wedge product as 1/2(ab-ba) because unless both a and b have an odd grading, in general. Phys 11:01, 21 Aug 2003 (UTC)
- Replacing vector spaces and algebras over the complex numbers with algebras over real Clifford algebras achieves just exactly what? Sure, any quantity whose square is -1 and commutes with everything can be thought of as for all intents and purposes as i, but choosing the n-vector for an n-dimensional space as i doesn't really make any difference. It doesn't really matter what i "really" is. Insisting it's a certain element of a Clifford algebra doesn't really matter. It's already well-known that in many fields like quantum mechanics, we could simply deal with real algebras and real vector spaces provided we define an element in the center whose square is -1. Phys 14:00, 21 Aug 2003 (UTC)