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I'm having an issue seeing how these octet states are reproduced via SU(3) transformations, in my notes it is written:

"Now, the remaining 8 states in (25) mix into each other under SU(3) transformations. For example just interchange two labels such as R<->B and you'll see these mix"

I'm not exactly sure what he means by interchanging the labels, equation (25) reads:

[tex]R\bar{R},G\bar{G},B\bar{B},R\bar{G},R\bar{B},B\bar{G},B\bar{R},G\bar{R},G\bar{B}[/tex]

and one of these states is a singlet (i.e. colour neutral state) which is given by

[tex]\frac{1}{\sqrt3}(R\bar{R}+B\bar{B}+G\bar{G})[/tex]

anyway he interchanges the labels R and B and finds you get the octet states

[tex]\frac{1}{\sqrt2}(R\bar{R}-B\bar{B}),\frac{1}{\sqrt6}(R\bar{R}+G\bar{G}-2B\bar{B}),R\bar{G},R\bar{B},B\bar{R},B\bar{G},G\bar{R},G\bar{B}[/tex]

But I can't exactly see how we get these states by an interchange (but then again I'm not exactly sure what is meant by an interchange of labels) - it's using the SU(3) transformations obviously but I'm not sure how I'd set up the above 'mathematically' or 'matrix-ically'!

Anyway probably obvious but I'm slow,

Thanks in advance!

SK

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# Colour Octet States

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