What Is the Role of Color Charge in Strong Interactions?

[Poirot]

Homework Statement

In electromagnetic interactions, the force carrier is the photon, and it interacts with anything which has electric charge. Electric charge can be represented by the integers on a single number line and photons themselves carry no electric charge.
(a) In the case of the strong interaction, explain what is analogous to the number line representing electric charge in electromagnetism.
(b) Do gluons carry the charge associated with the strong interaction?
(c) What important feature of the strong interaction follows from your answer to (b)?

Homework Equations

The Attempt at a Solution

(a) The colour charge associated with gluons? (this is the one I'm not sure of, what does this mean?)
(b) Yes- colour charge
(c) Colour charge is conserved in strong interactions.

Thanks for any help with a), and if the other are correct.

 

[mfb]

(a) The colour charge associated with gluons? (this is the one I'm not sure of, what does this mean?)
(b) Yes- colour charge

Right. For (a), you can be more precise. Can you draw color charges on a line like you can with electric charges where you have integers?

(c) Colour charge is conserved in strong interactions.

Why would that follow from gluons carrying color charge? Photons do not carry electric charge, but electric charge is conserved.
Color charge is conserved, but that is not the result of (b).

 

[Poirot]

Right. For (a), you can be more precise. Can you draw color charges on a line like you can with electric charges where you have integers?Why would that follow from gluons carrying color charge? Photons do not carry electric charge, but electric charge is conserved.
Color charge is conserved, but that is not the result of (b).

For (a), I think you can, in the sense that there are 8 possible colours for gluons so it's discrete up to a point?
and for (c) Is this getting at the fact that as gluons carry colour charge, they have self interactions, unlike photons?

Thanks again, forever grateful!

 

[mfb]

For (a), I think you can, in the sense that there are 8 possible colours for gluons so it's discrete up to a point?

The gluons are not the point. What about the color charges themself? Is there a color charge "1"?

and for (c) Is this getting at the fact that as gluons carry colour charge, they have self interactions, unlike photons?

Yes, self-interaction is the first point, but you can add a second step. What is an important consequence of the self-interaction?

 

[Poirot]

The gluons are not the point. What about the color charges themself? Is there a color charge "1"?
Yes, self-interaction is the first point, but you can add a second step. What is an important consequence of the self-interaction?

For (a) There are 6 colour charges, red, green and blue and their anti's, but with electric charge there's, for example, +1 or -1 which are the same kind of charge differing in sign. But with colour charge, they are different? Is this maybe getting at as there are 6 types (3 and their anti's) so you can represent them on 3 number lines of integer colour charge?

For (c) Is it that gluon-gluon interactions leads to quarks being bound in hadrons and they cannot exist in free states on their own? I don't really understand why this is, I have just read it.

 

[mfb]

so you can represent them on 3 number lines of integer colour charge?

It goes in the right direction, but you also have gluons with one color and one anticolor, or quarks with a superposition of colors, so you need more than just the three lines. Not more lines, but something ... bigger.

For (c) Is it that gluon-gluon interactions leads to quarks being bound in hadrons and they cannot exist in free states on their own? I don't really understand why this is, I have just read it.

Yes. Self-interaction alone is not sufficient for this, but it is the critical point.

 

[Poirot]

It goes in the right direction, but you also have gluons with one color and one anticolor, or quarks with a superposition of colors, so you need more than just the three lines. Not more lines, but something ... bigger.

Is it some kind of coordinate system or matrix? Then you could effectively 'plot' where the points are? Thank you for all the help by the way, I only have half a page of notes on gluons/strong interaction from lectures and most of this stuff isn't covered.

 

[mfb]

s it some kind of coordinate system or matrix? Then you could effectively 'plot' where the points are?

You can treat the colors as coordinates in space, that is the main point. You are not limited to the axes.