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

[Marty4691]

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.

 

[Vanadium 50]

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.

 

[Marty4691]

Thanks for your help.