Redundancy in QCD: Is su(4)=su(2)xsu(2) Possible?

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SUMMARY

This discussion centers on the potential redundancy in Quantum Chromodynamics (QCD) regarding the gauge group representation. The question posed is whether so(4) can replace su(3) as the gauge group for QCD. Key observations include the relationship between su(3) and so(4), where setting λ3 and λ8 to zero yields so(4), and the nature of gluons associated with these parameters. The consensus is that such a substitution is not viable, as established by LEP findings confirming three colors and eight gluons in QCD, which would be compromised by adopting so(4).

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Marty4691
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I guess my question is really: is there redundancy in QCD. In particular, is it possible to use so(4)=su(2)xsu(2) as the gauge group for QCD instead of su(3). I only have a couple of qualitative observations to suggest this speculation.

The first is the relationship between su(3) and so(4). If you take su(3) and set λ3 and λ8 to zero you end up with so(4). It's overstating, but one might say that so(4) is a "special case" of su(3).

The second is the form of the gluons corresponding to λ3 and λ8. Unlike the other six gluons they appear to be colorless. Are these gluons necessary? It seems like hadrons and mesons might still be held together by the other six gluons.

Thanks for your time.
 
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The answer is no. We know from LEP that there are 3 colors and 8 gluons, not 4 and 6.

Also, such a theory would break QED.
 
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Thanks for your help.
 

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