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## Main Question or Discussion Point

QCD has 3 "colors". I'm wondering whether there is something special about the number 3, or whether it is possible to generalize to N colors and get a very similar theory.

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QCD has 3 "colors". I'm wondering whether there is something special about the number 3, or whether it is possible to generalize to N colors and get a very similar theory.

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Vanadium 50

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Yes, you can. But what you get doesn't have anything to do with reality.

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I was just asking about the theory. You have to actually understand the implications of a theory to know whether it has anything to do with reality.Yes, you can. But what you get doesn't have anything to do with reality.

For example: Is QED the same as N=1 QCD? Is electroweak theory the same as N=2 QCD (plus the Higgs)?

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The Abelian gauge group with the gauge group U(1) is the most simple one. An example is QED.

The non-Abelian case is a bit more restrictive. The gauge fields are necessarily self-interacting on the tree level and thus all particles must couple with the same universal coupling strength (coupling constant [itex]g[/itex]) in order to not to destroy the symmetry.

QCD is based on local SU(3) color symmetry. There is nothing special in the number 3 but it's an empirical fact that there are three colors in nature. It can be pretty directly seen on the plot of the [itex]e^+ + e^- \rightarrow \text{hadrons}[/itex] cross section, usually plotted normalized to the QED-tree-level cross section for [itex]e^+ + e^- \rightarrow \mu^+ \mu^-[/itex]. You find it, e.g., here (on page 6):

http://pdg.lbl.gov/2013/reviews/rpp2012-rev-cross-section-plots.pdf

The electroweak sector is based on the gauge group SU(2) x U(1) but somewhat different from QCD in the sense that the gauge group is "Higgsed", i.e., spontaneously broken to U(1).

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http://en.wikipedia.org/wiki/1/N_expansion

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