Clarifying Fradkin's Terminology on Quantum Numbers of Gauge Groups

The Wilson loop, being a charged operator, transforms non-trivially under gauge transformation and follows the conjugation law for the fundamental representation. The quantum numbers refer to the charges associated with each gauge group generator. In summary, Fradkin in "Quantum Field Theory an integrated approach" discusses the concept of Wilson loops carrying the quantum numbers of the representation of the gauge group. This means that they are charged operators, transforming under gauge transformations and following the conjugation law for the fundamental representation. The quantum numbers refer to the charges associated with each gauge group generator.
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paralleltransport
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TL;DR Summary
I'd like to clarify some terminology
Hi, I'd like to clarify the following terminology
(Fradkin, Quantum Field Theory an integrated approach)
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"carry the quantum numbers of the representation of the gauge group":
Does the author basically mean that the wilson loop is a charged operator, in a sense that it transforms non-trivially under gauge transformation:
W -> U(x) W U(x)^{-1}

Furthermore, the fact that the wilson loop transforms under the fundamental representation means that it is just a N x N matrix for SU(N) gauge field and transforms according the conjugation law above?

Finally, the so called "quantum numbers" are then just the charges associated with each gauge group generator?
 
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Yes, I think that's what Fradkin means.
 

1. What is the significance of Fradkin's terminology on quantum numbers of gauge groups?

Fradkin's terminology is important in the field of quantum physics as it provides a systematic way to label and classify the different quantum states of a gauge group. This terminology helps in understanding the symmetries and properties of these quantum states.

2. How does Fradkin's terminology differ from other systems of labeling quantum numbers?

Fradkin's terminology differs from other systems in that it uses a combination of letters and numbers to label the quantum states, rather than just numbers. This allows for a more comprehensive and organized classification of the states.

3. Can Fradkin's terminology be applied to all gauge groups?

Yes, Fradkin's terminology can be applied to all gauge groups, including both Abelian and non-Abelian groups. It provides a universal framework for labeling quantum states regardless of the specific gauge group involved.

4. How does Fradkin's terminology help in the study of gauge theories?

Fradkin's terminology provides a clear and consistent way to label and describe the quantum states of gauge theories. This allows for a better understanding of the symmetries and properties of these states, which is crucial in the study of gauge theories.

5. Are there any limitations to Fradkin's terminology?

One limitation of Fradkin's terminology is that it can become quite complex for larger gauge groups with many quantum states. Additionally, it may not be applicable to certain exotic gauge groups that have not yet been fully explored.

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