ANON CONTRIBUTED TO THIS PAGE, PLEASE LET IT STAND AS IS. Thanks, -- Doug

''Clifford Algebra Applications cover many areas in physics and engineering.'' -- JohnFletcher
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'''Example use of CliffordAlgebra'''

For Maxwell's equations, there are several simple ways to express them using Clifford algebras. The simplest is probably the one in Cl(3,1): http://php.jonnay.net/OpenWikiGraphics/math2/del.gif'''F''' = '''J''' which decomposes into two separately graded parts with http://php.jonnay.net/OpenWikiGraphics/math2/del.gif''''''http://php.jonnay.net/OpenWikiGraphics/math/and.gif '''F''' = 0 and http://php.jonnay.net/OpenWikiGraphics/math2/del.gif. '''F''' = '''J'''.

I would guess the 4th dimension is only different from the others if you deliberately base your algebra on a non-positive definite space. Also, shouldn't the 2-D case have pseudoscalars rather than pseudovectors? Personally I find the whole thing much more confusing than group representations, but there are enough people who swear by it that I'm undoubtedly missing something clever.

''For more discussion of this see HestenesOerstedMedalLecture p.16 and p.25-26'' -- JohnFletcher
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''I am attempting to apply this algebra to problems in chemical engineering and would be interested to hear from anyone else who is working on applications in thermodynamics or fluid mechanics. I put some papers which I gave at at the AGAGSE conference in July 2001 on the web at http://www.ceac.aston.ac.uk/clifford/index.html'' -- JohnFletcher
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Note on maths character: [''http://php.jonnay.net/OpenWikiGraphics/math2/del.gif is nabla, UniCode u2207, the field operator.'']
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See also CliffordAlgebra
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CategoryMath