As an aside, possibly related, the quarks of su(3) are usually written as (1,0), (1/2,+sqrt(3)/2), (1/2,-sqrt(3)/2). This is nice in that it uses only 2 degrees of freedom, that is, the quantum numbers for color.

But a more elegant version of su(3) is to use (1,0,0), (0,1,0), and (0,0,1) where these mean (red,green,blue) and eliminate the extra dimension by letting red+green+blue = 0.

And an alternative way of doing the same thing is to use (+1,-1,0), (-1,0,+1), (0,+1,-1). This is very similar to the weight code words you’re discussing.

These are the quantum numbers for the 3 colors. The quantum numbers for the white state is of course (0,0,0).

]]>the notion of rig allowing to represent algebraic numbers resulting as roots of polynomials with positive natural numbers as coefficients generalizes by replacing natural numbers by p-adic integers: this means that one allows also “super-naturals” identified as p-adics infinite as real numbers.

One obtains * all* complex algebraic numbers as cardinalities and in some cases the algebraic functions involved converge also for some p-adic number fields so that set theoretic representations of the object as as p-adic fractal is possible as discussed in the first posting. In particular, the Golden Object of John Baez exists 2-adically.

See the posting at my blog and its predecessor.

]]>