# Is color charge a quantum mechanical observable?

If I had 2 pions that were identical, except one was comprised of a red and anti-red, and the other was comprised of a green and anti-green, would I be able to perform an experiment that distinguishes between them?

## 1 Answer

Color charge in the sense of "being blue, red, green" is not a quantum mechanical observable because the $\mathrm{SU}(3)$ gauge transformations mix the colors. This means it is meaningless to say "We have a blue particle", because we can perform a gauge transformation and then we "have a red particle". Since physical descriptions related by gauge transformations are equivalent, there is no difference between "having a red particle" and "having a blue particle". You cannot, even in principle, determine the "color" of an object in this sense.

The popular phrasings of "red, blue and green" quarks are actually meaningless. They give a nice heuristic because the "color language" gives a way to draw many intuitive conclusions about otherwise unintuitive group theory, but "red, blue or green" quarks do not exist. Objects in the theory that are related by a gauge transformation are literally the same, there is no difference between a "red quark" and a "green quark" - a quark is a quark is a quark.

What we are able to say (if you manage to deconfine the color-charged stuff, since confinement means that we only see colorless objects) is "I have a color-charged particle", and specify "which kind of color charge" it has, i.e. whether it has merely a color (like quarks), or a color-anticolor (like gluons), or color-anticolor-anticolor (like nothing we know), and so on. (These correspond formally to different $\mathrm{SU}(3)$ representations) This - "color/color-anticolor/color-anticolor-anticolor/..." - is the proper generalization of the $\mathrm{U}(1)$ electric charge to non-Abelian gauge theories.

• so, are there any reference color, similar to -ve for electron? and is linear combination of color also color under su3? – unsym Apr 16 '15 at 15:15
• @hwlau: I just realized that that point of my answer is wrong. – ACuriousMind Apr 16 '15 at 15:18
• It should be pointed out that a gauge transformation affects the gluons too and not just the quarks. That's what stops you from comparing two quarks at different points by bringing them to the same point---the gluon field conspires to ensure the quarks' colours change as they move. – Brian Bi Apr 17 '15 at 4:23
• Is this also true about electric charge? If so is that why we never talk about an object being in a superposition of positive and negitive charge? Or have I never heard of a superposition of positive and negitive charge? – Shane P Kelly Jan 10 '16 at 2:00
• @Shane: No, positive and negative charge are not the analogue to the colors red, green, blue, but to the representations "color", "color-anticolor", and so on. The electromagnetic gauge transformations just "rotate a phase", they do not mix positive and negative. – ACuriousMind Jan 10 '16 at 14:35