Gluon octet

[Xibalba]

Hi, I was wondering how to calculate the probability of the color charge of a gluon from its equation/name.

I understand that a gluon (rab+bar)/sqr2 has 50% chance to carry the red-antiblue (rab) color, and equal chance to carry the blue-antired (bar) charge.

But what about those with a minus sign between the two?
And those with a -i number in front of the parenthesis?
And the last one with three "possibilities"?

Check here to see what I'm talking about : Eight Gluon Colors

Thanks

[Xibalba]

Help please I suck at statistics...

[Cougar]

And those with a -i number in front of the parenthesis?

I'm guessing this indicates a rotation of 90^o.

[grapes]

I'm guessing this indicates a rotation of 90^o.

I'm kinda intrigued by the comment

there are many ways of presenting these states

I mean, why write them as:

and

Instead of: and

Saves a minus sign. :)

I guess, red comes first.

[Xibalba]

I'm guessing this indicates a rotation of 90^o.

Would that be related to the spin of the gluon? Gluons have spin=1, and I don't think it can be -1.

However, I do know there are some kind of polarization, similar to the polarization of light, that can be happening, but I don't know how to imagine that.

[Shaula]

The i is there to ensure the gluon states meet the commutation criteria for the Gell-Mann matrices, which ensures they are representing an SU(3) symmetry. Likewise the reason behind the notation is that they are usually written so that each state is a sum of these elements in the 'order' they appear, IIRC.

Been a while since I did this!

[Xibalba]

The i is there to ensure the gluon states meet the commutation criteria for the Gell-Mann matrices, which ensures they are representing an SU(3) symmetry. Likewise the reason behind the notation is that they are usually written so that each state is a sum of these elements in the 'order' they appear, IIRC.

Been a while since I did this!

Then, could you shed a light on how can we, science enthusiasts, can make an image of each of the eight possible gluons in our mind? If the notations are only to fit the matrices, then what differenciates them apart?

[ShinAce]

The first thing you'll need is linear algebra. From that point of view, the matrix is saying that any solution is the combination of eight independent, or different, possibilities. In other words, if i remove one of the eight 'pieces' i can't make it out of the 7 remaining 'pieces'. Kind of like if Lego only had 8 different kinds of blocks. The gluons aren't the lego blocks, they are what you can build with those blocks. I would not dare explain to a pirate how his ship can be modeled from eight different types of pieces.

Now, going from that to a mental picture of how these lego pieces come together doesn't make sense. The 'possibilities' are colors and add using bizarre rules which results in a force. Even something likr charge which is so familiar is hard to imagine. It's a fundamental property, that's why you can't build up to it using everyday happenings.

[Shaula]

The colour octet describes the colour charge of the gluon, as Shin Ace says the basic point is that there exist 8 fundamental units of colour charge from which all allowed combinations can be made. These 8 colour charges correspond to the octet. The reason they are written like that is that there are constraints on how these charges can be modelled relating to how they can be added (no singlet states).

To be honest trying to imagine QCD without delving into mind-hurting maths is really misleading. I am not an expert at all, just know just enough to be scared.