Re: vector products

[Jack Uretsky <jlu@HEP.ANL.GOV>]

Hi Tina-
        Most people who've been in physics graduate courses have been
exposed to Clifford algebras.  Two popular Clifford algebras are the
algebra of the Pauli matrices and the algbra of the Dirac matrices.
Mathematicians first (I think, I haven't checked) first encountered a
Clifford algebra in the algebra of quaternions.
        John Denker's use of the wedge product to discuss the product AB
of two vectors has a realization as follows, in the Pauli algebra.
Let s stand for the vector whose components are the 3 Pauli (spin)
matrices, and A and B two ordinary vectors (meaning 3-component objects).
Then let (A/) be the dot product A.s, and similarly with (B/).
        Then John's product (A/)(B/)=A.B+iAxB.s, where i=sqrt(-1).  The
second term may be replaced with the "wedge product" to the same effect.
        I first encountered wedge products when I read Misner, Thorne and
Wheeler's book on gravitation while practicing law full time.
                                        Regards,
                                                Jack
On Mon, 26 Aug 2002, Tina Fanetti wrote:

> What in the world is the wedge product?
> How am I supposed to explain Clifford Algebra when
> 1.  I don't know what it is.
> 2.  Most of my students are in Calc 1.
> 3.  The last time my students saw geometry they were in high school.
>
> I looked in my favorite book, div, grad, curl and all that and the we=
> dge product isn't in there.
>
> My Arfkin book is at home, maybe it is in there...
>
> Tina
>
> Tina Fanetti
> Physics Instructor
> Western Iowa Technical Community College
> 4647 Stone Ave
> Sioux City IA 51102
> 712-274-8733 ext 1429

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