I Charge Operators & Electric Charge - Wikipedia

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In the wikipedia article about Charge, it says that when the symmetry group is a Lie group, then the charge operators correspond to the simple roots of the root system of the Lie algebra. So for U(1) group, how do the simple roots show that the charge in question is the electric charge?
 
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Superfluid universe said:
So for U(1) group, how do the simple roots show that the charge in question is the electric charge?

I'm not sure what you mean. Electric charge is defined as the charge associated with the U(1) symmetry of the electromagnetic interaction.
 
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Hello, thank you for replying to me. :)
Well, i mean how does the charge "correspond" to the simple roots then?
 
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Thanks for replying to me, Peter. I get that it is complicated, but is there any way of explaining it a bit simplified? At least what they mean by "correspond to".
 
Superfluid universe said:
is there any way of explaining it a bit simplified?

I don't know that there is.

Superfluid universe said:
At least what they mean by "correspond to".

Note that the article says the charge operators correspond to simple roots, not the charge quantum numbers. The charge quantum numbers (i.e., things like ##-1## for the electron) correspond to weights of representations. Not that that necessarily simplifies things, but it should make clear that there are two different correspondences involved, because there are two different concepts associated with "charge", the operators (things that act on states) and the quantum numbers (the numbers you get when you act on states with charge operators).
 
"Note that the article says the charge operators correspond to simple roots, not the charge quantum numbers."

Ah, i thought they used "charge operator" and "charge" as synonyms. Thanks for engaging with me.
 
Superfluid universe said:
May I ask if there are more quantum numbers than stated in this article?

Look at the section of the article titled "How many quantum numbers exist?".
 
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Yes, i read that paragraph. But since they didn't give any examples of other quantum numbers, i asked you. :)
 
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