Clifford Algebra Details

CliffordAlgebraDetails is a page with some of the detailed stuff from CliffordAlgebra. This needs more attention which I am giving it bit by bit. -- JohnFletcher
Some Information


Notation for the basis vectors


Geometrical Interpretation

It is sometimes reasonable to regard basis vectors that square to -1 as indicating negative curvature in the dimensions in question. See also WickRotation (e.g. http://en.wikipedia.org/wiki/Wick_rotation and discussion on blog of string theorist LuboŇ° Motl (pronounce: "Loo-bosch Maw-tull") at http://motls.blogspot.com/2005/02/wick-rotation.html, and a different blog with discussion of Motl at http://www.math.columbia.edu/~woit/blog/archives/000160.html which includes the amusing comment, "Do you think it's statistically significant that the two most prominent string theorists with weblogs are both incredibly arrogant and incapable of admitting that anyone who disagrees with them might have a point?" -- DougMerritt
This part needs revision as there are some errors in it. -- JohnFletcher
Can someone who remembers all this better than I do, fill in the details? There was something terribly clever about expressing all Maxwell's equations in four symbols, or something. -- PeterHartley
The problem is that for each "dimensional" entry in the table above, there are several choices.

Cl(2) is actually isomorphic to the quaternions, not Cl(3), though Cl(3) has several sub-algebras isomorphic to the quaternions. Of the 1-d Clifford algebras, one is described above, and the other is isomorphic to the complex numbers.


Some general comments not yet revised, was originally on CliffordAlgebra.


See also CliffordAlgebra
CategoryMath

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