File talk:A2example.pdf

Weight diagrams for su(3) irreps and “graphical conventions”
This picture is useful to illustrate the “extra“ features that appear in su(3) representations, as compared to the su(2) ones that physicists are familiar with from angular momentum. However, the picture is at odds with a few “standard conventions“ that I found in nearly all the books (well, the physics-oriented ones that care about drawing diagrams for su(3) multiplets and irreps).

An encircled point often means that this point in the I_3 Y-plane appears twice (multiplicity > 1). Or one puts two dots nearby. In the picture, the encircled point is just meant to highlight some point, perhaps the ket with the “highest weight“, or the ket in the first “Weyl chamber“. (Both concepts are familiar for people from representation theory, but less familiar for the “working physicist“.) Also, the picture uses a number two to indicate the multiplicity.

The axes of the multiplet plane are along the isospin I_3 (horizontal) and the hypercharge Y (or strangeness), vertical. They correspond to the eigenvalues of the Gell-Mann matrices lambda_3 and lambda_8. This means that a multiplet has "horizontal" lines formed by multiplets of the su(2) isospin subgroup (in the article Clebsch-Gordan coefficients for SU(3): the generators T_3, T_plus, T_minus). Depending on whether the diagram is for the irrep (2,1) or (1, 2), the picture should have a horizontal top row with three or two kets. The picture does not respect this choice.

Here is a picture that is closer to these “physicists'” conventions.

DieHenkels (talk) 13:48, 23 November 2023 (UTC)