ATON is a hopefully evolving classification theory. It aspires to unify knowledge around numbers and prefers naive methods. Some of the older posts are wrong but I'll keep them for the sake of continuity.

Wednesday, April 12, 2006

SU(2)

SU(2) is the symmetry of the weak force and has a base of 3 2*2 complex matrices with unit determinant;
((0,1),(1,0))
((0,-i),(i,0))
((1,0),(0,-1))
They all square to the unit matrix;
((1,0),(0,1))
SU(2) is like an extention to complex numbers.

SU(2) compares to E2/H2={,{}}/{,{,{}}} with the state quotient SE2/SH2=2/4=1/2.
Consider the collapsing iteration of H2;
{,{,{}}}
[,{,{}}]+[{,{}},]
[,[,{}]]+[,[{},]]+[[,{}],]+[[,{}],]
The collapse of {} gives only one state [], like +1-1=0.
H2 has a 2*2 form when collapsed, like a 2*2 matrix.
As I noted before, E2=H1={,{}} compares to Complex numbers.
{,{}}
[,{}]+[{},]
Thus E2/H2 is interpreted as "E2 for given H2".

Modular group has also 2*2 form and obeys a condition similar to unit determinant.
((a,b),(c,d)) with ad-bc=1.
DNA has a similar form with 2*2 bases.

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