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For the benefit of those afflicted with browsers that
can't display the symbol font, I put up a DJVU version
of the Clifford Algebra / Maxwell equations exercise,
namely:
http://www.monmouth.com/~jsd/physics/maxwell-ga.djv
You may need to download a free DJVU plugin from
http://www.lizardtech.com/download/?f=0&d=1
The content remains the same, namely:
I recently did an amusing exercise. Starting from
the equations of electromagnetism in the form
del F = 4pi J
I turned the crank on the Clifford Algebra to confirm
that it does indeed regenerate the old-fashioned vector
representation of Maxwell's equations.
It was an interesting tour of the Geometric Algebra
machinery. I wrote up some notes on the scenery
along the way, including some of the pitfalls that
one learns to avoid.
Using cross products is like eating soup with a fork.
Clifford Algebra is the spoon -- it's easier and gives
a better result.