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The Gluon Octet

  1. Feb 27, 2012 #1
    Below are 2 states in the gluon octet.

    What is the difference between:

    42d661c64cea488ab431b5c9aac3fa96.png

    and

    e34377f3be0d54c79320e2883f05dc34.png

    What do these equations represent?
     
  2. jcsd
  3. Feb 27, 2012 #2

    Ben Niehoff

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