Where are gluons present
If gluons are two-colored and there are three possibilities for each color, then, according to Adam Riese, there should also be nine gluons. Or?
It is not so. In order to find out the reason for this, one has to be familiar with quantum theory and what is known as group theory.
Combinations in quantum theory According to quantum theory, on the one hand, one must not only consider the nine possibilities mentioned above, but also take into account all combinations that result from addition and subtraction - for example: 1 / root (2) (red- Anti-red - green-anti-green).
Group formation in group theory On the other hand, the theory of strong force is a calibration theory, i.e. it is based on the fact that it doesn't matter what color we call red, blue or green. We could also rename it without affecting the behavior of the quarks. So there is a symmetry and mathematically symmetries are described with the help of group theory.
The results of the group theory together with the combination formation of the quantum theory now result in the following nine possibilities for the gluons:
1 / root (2) (red-anti-red - green-anti-green),
1 / root (6) (red-anti-red + green-anti-green - 2 blue-anti-blue) and
1 / root (3) (red-anti-red + green-anti-green + blue-anti-blue)
The colors of the ninth gluon cancel each other out exactly: This so-called color singlet is colorless and does not play a role in the transmission of the strong force. Because it depends on the color.
So after all the math, there are only eight gluons left. The colorless falls by the wayside.
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