Robert G. Brown
Fri May 12 01:59:00 GMT 2006
On Thu, 11 May 2006, Linas Vepstas wrote:
> I demand that Robert G. Brown are belonging when Thu, May 11, 2006 at 01:30:43PM -0400:
>> doing Geometric Algebra, by the way.
> I thought geometric algrebra was just for 3D space and mosly aimed at
> college students; are you implying that there's a geometric algebra
> vocabulary for general Clifford algebras and/or supersymmetry? Does
> it get used much in the broader context?
Geometric algebra is the modern name for a (geometric interpretation of
a) Clifford algebra. Perhaps it also fixes up a few things Clifford
didn't do quite right and makes it fully extensible. There is a fairly
succinct Wikipedia article on it. If you want to see more, Doran and
Lasenby is a FABULOUS book if you've ever studied Grassmann and Clifford
algebras etc. When I was back in grad school, we "knew" that these
things were important and being done "wrong", but subsequently they've
been fixed up and are now being done right. The importance (beyond the
obvious embedding of all sorts of basic equations and physical theories
in the algebra, e.g. Maxwell's equations) remains to be demonstrated,
at least in reference to e.g. supersymmetry at least as far as I know
(which isn't too far:-).
That's why I am hesitant about seeing quaternions done out of context,
as it were. If anybody ever does decide to do a real Clifford/Geometric
algebra package with the grade (dimension) of the algebra basically a
free input parameter, it would both include quaternions as a particular
grade and would probably represent them slightly differently. Of course
the same could be said about complex.
Robert G. Brown http://www.phy.duke.edu/~rgb/
Duke University Dept. of Physics, Box 90305
Durham, N.C. 27708-0305
Phone: 1-919-660-2567 Fax: 919-660-2525 email:firstname.lastname@example.org
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