What are the states and equations of the Gluon Octet in SU(3)?

[Michio Cuckoo]

Below are 2 states in the gluon octet.

What is the difference between:

and

What do these equations represent?

 

[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).