User:Jheald/sandbox/GA

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Current targets:

  • The mixed multivector ((sin(θ) + cos(θ) e1), created by the "flattening" the e3 direction on right-multiplying by the primitive idempotent (1+ e3). What does this mixed multivector mean? Why might projective space be a clue?
  • Conformal geometric algebra -- as the place to look, so see what projective transformations come up
  • Weyl & Brauer's decomposition of rotations -- what exactly were their steps, & how did their spinors get used?
  • "Isotropic space" -- i.e. (most often) one with mixed signature. Why are Cartan's spinors considered so embedded in such a space? Is there a relation with Cl+(p,q)Cl(p-2,q+1).
  • The non-columnlike reappropriation of the word "spinor" by several GA books: document,
  • "Geometric algebra" vs. "Clifford algebra" -- write up results of reading survey for Talk:Geometric algebra.


Scratchpad for pages where adding a GA perspective might be useful, or where existing GA material might usefully be tweaked.

  • Bott periodicity -- off-puttingly mathematical at the moment. Some more general remarks/conclusions would be good to float higher up, to give people an idea of what it means. (Is the pseudo-scalar the key to this? eg: its square, square of its reverse, etc; also chirality).
  • Pauli matrices -- add more physics?
  • Clifford module -- what is this?
    • We used to have an explicit construction somewhere for representations of Clifford algebras / spin matrices -- where did it go?
Found it: [4]; was rm'd from the page as "nonstandard". Not all the representations are faithful (a.k.a. "universal" in the language of the page)
Instead there are Higher-dimensional gamma matrices and Weyl–Brauer matrices.
Woit [5] introduces a "Mathematical finds" by Baez [6]

Some good GA pages[edit]

Websites[edit]

  • [8] Czech page with good bibliography / links


GA contributors[edit]

also try