Re: Desperately Seeking Spinors

Matej Pavsic wrote:

Now, instead of the basis which consists of a scalar, vectors,
bivectors, 3-vectors, and 4-volume, one can consider an alternative
basis of 16 independent "mixed" grade elements. They can be formed by
four independent Clifford numbers P_k, k =1,2,3,4, whose squares are
zero:

P_1 = (1/4) (1 + \gamma_0)(1 + i \gamma_{12})
P_2 = (1/4) (1 - \gamma_0)(1 + i \gamma_{12})
P_3 = (1/4) (1 + \gamma_0)(1 - i \gamma_{12})
P_4 = (1/4) (1 - \gamma_0)(1 - i \gamma_{12})
Here \gamma_{12} is the same as \gamma_1 \gamma_2. Analogously
for \gamma_{123}, etc., and i is the usual imaginary unit.

Sorry for a lapsus. The objects above are idempotents
satisfying P_1 P_1 = P_1, etc.
I wanted to avoid the technical jargon, but unfortunately I did a blunder
when commenting the above idempotents: I wrote that their squares
are zero (this was because I am so often working with
nilpotent objects as well).

.