# The Gluon Octet

1. Feb 27, 2012

### Michio Cuckoo

Below are 2 states in the gluon octet.

What is the difference between:

and

What do these equations represent?

2. Feb 27, 2012

### Ben Niehoff

$r, g, b$ are basis vectors in the fundamental rep of SU(3) (i.e., column vectors). $\bar{r}, \bar{g}, \bar{b}$ are basis vectors in the anti-fundamental rep (i.e., row vectors). Terms like $b \bar{r}$ are outer products. Each of the expressions you wrote is an element of the Lie algebra $\mathfrak{su}(3)$ (i.e., a 3x3 matrix).