Is $X=a^2+b^2+c^2+d^2+e^2+f^2$ an invariance group of $SU(3)$?

69 Views Asked by Bumbble Comm At 04 Apr 2026 - 8:36

On page 7 of the following paper,

the author seems to imply that an expression of 6 independent variables such as:

$$ X = a^2+b^2+c^2+d^2+e^2+f^2 $$

has invariance group SU(3).

Can anyone explain how the addition of six squares is related to SU(3).

In the case of SU(2), I can see that

$$ S=S_x\sigma_x + S_y\sigma_y + S_z\sigma_z\implies S^2 = S_x^2+S_y^2+S_z^2 $$

But su(2) is associated to 3 matrices and su(3) to 8 matrices. Why $X$ has 6 terms and not 8?