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

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In summary, the conversation discusses the possibility of using so(4)=su(2)xsu(2) as the gauge group for QCD instead of su(3). The first observation suggests that so(4) is a "special case" of su(3), while the second observation questions the necessity of two specific gluons. However, it is stated that there are 3 colors and 8 gluons in QCD, not 4 and 6. Additionally, such a theory would break QED.
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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.
 

1. What is redundancy in QCD?

Redundancy in QCD refers to the fact that certain mathematical representations of the theory may be equivalent to others, leading to multiple ways of describing the same physical phenomena.

2. How does su(4)=su(2)xsu(2) relate to redundancy in QCD?

The equation su(4)=su(2)xsu(2) suggests that the mathematical representation of su(4) may be equivalent to the product of two su(2) representations, leading to a potential redundancy in the theory.

3. Is su(4)=su(2)xsu(2) a valid representation for QCD?

This is currently a topic of debate and research in the field of QCD. While some studies have shown that it is possible, others suggest that it may not fully capture the complexity of the theory.

4. What are the implications of su(4)=su(2)xsu(2) being a valid representation for QCD?

If su(4)=su(2)xsu(2) is proven to be a valid representation for QCD, it could potentially simplify calculations and provide a more elegant description of the theory. However, it would also require further investigation and validation to ensure it accurately reflects the physical reality.

5. How does the concept of redundancy in QCD impact our understanding of the theory?

The presence of redundancy in QCD highlights the complexity of the theory and the need for continued research and refinement. It also raises questions about the most accurate and efficient ways to mathematically represent and study QCD.

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