Why 8 Gluons?
Why 8 gluons?
As far as I know, gluons have a color charge, it is the combination
of a color ith an anticolor.
I have read in many places that due to SU(3) simmetry properties,
there are only 8 gluons, but I can't figure out wich one are them.
Using a simple combination, gluons could be red-antiblue, red-
antigreen, red-antired, blue-antired, blue-antigreen, blue-antiblue,
green-antiblue, green-antired and green-antigreen. (9 kinds of gluons)
Since three of them have a white color (red-antired, blue-antiblue
and green-antigreen) I can eliminate them, but then I only have 6
Where does the number 8 come from?
To be truly white, the gluon must be red-antired, green-antigreen, AND
blue-antiblue. Based on the mathematics of wave function probability, the
white gluon is (red-antired + blue-antiblue + green-antigreen)/sqrt(3). The
square root of three is to keep things the correct size. There are tow wave
functions that are not actually white: (red-antired -
green-antigreen)/sqrt(6) and (red-antired + green-antigreen -
2*blue-antiblue)/sqrt(6). These two gluons can interact without changing
the color of a quark, but they are not truly white. A white particle can
have no preference for red, green, or blue.
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Update: June 2012