Editing Gluon (section)

=== Eight color states ===
<!-- the link "eight gluon types" from the article "Quark" links here -->
There are eight remaining independent color states corresponding to the "eight types" or "eight colors" of gluons. Since the states can be mixed together, there are multiple ways of presenting these states. These are known as the "color octet", and a commonly used list for each is:<ref name="Griff"/>

: {|
|-
|<math>(r\bar{b}+b\bar{r})/\sqrt{2}</math>
|&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
|<math>-i(r\bar{b}-b\bar{r})/\sqrt{2}</math>
|-
|<math>(r\bar{g}+g\bar{r})/\sqrt{2}</math>
|
|<math>-i(r\bar{g}-g\bar{r})/\sqrt{2}</math>
|-
|<math>(b\bar{g}+g\bar{b})/\sqrt{2}</math>
|
|<math>-i(b\bar{g}-g\bar{b})/\sqrt{2}</math>
|-
|<math>(r\bar{r}-b\bar{b})/\sqrt{2}</math>
|
|<math>(r\bar{r}+b\bar{b}-2g\bar{g})/\sqrt{6}</math>
|}

These are equivalent to the [[Gell-Mann matrices]]. The critical feature of these particular eight states is that they are [[linearly independent]], and also independent of the singlet state, hence 3<sup>2</sup>&nbsp;&minus;&nbsp;1 or 2<sup>3</sup>. There is no way to add any combination of these states to produce any others. It is also impossible to add them to make ''r''{{overline|''r''}}, ''g''{{overline|''g''}}, or ''b''{{overline|''b''}}<ref>{{cite web  |author=J. Baez |title=Why are there eight gluons and not nine?  |url=http://math.ucr.edu/home/baez/physics/ParticleAndNuclear/gluons.html |website=math.ucr.edu  |access-date=2009-09-13}}</ref> the forbidden [[singlet state]]. There are many other possible choices, but all are mathematically equivalent, at least equally complicated, and give the same physical results.