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south
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- It's dimensions
Color charge is not scalar. Still, do their components have dimensions (in metrological terms)?
What do you mean by this statement? Can you state it in mathematical terms?south said:Color charge is not scalar.
Thank you Peter Donis for assisting mePeterDonis said:What do you mean by this statement? Can you state it in mathematical terms?
What article? Please give a reference.south said:I read an online article
Article:PeterDonis said:What article? Please give a reference.
Have you tried looking at actual textbooks, papers, or course notes on the Standard Model (there are plenty available for free online)?south said:
What do you mean by "in metrological terms"? You do realize that we cannot directly measure color charge since all observable particles are color neutral?south said:do their components have dimensions (in metrological terms)?
I haven't tried it. I'm momentarily interested in what kind of magnitude the color charge is, dimensionless or not.PeterDonis said:Have you tried looking at actual textbooks, papers, or course notes on the Standard Model (there are plenty available for free online)?
Ok, but then:south said:I simply add the adjective metrological to refer the meaning to the type of magnitude that is not dimensionless and that is quantitatively expressed including some unit of measurement.
There is no point in being "momentarily interested" in physics. Either you want to learn it, or you don't. If you do, it takes time, and is not best done by asking random questions that "momentarily" occur to you.south said:I haven't tried it. I'm momentarily interested in what kind of magnitude the color charge is, dimensionless or not.
Fundamentally, neither electric nor color charge has a dimension. In quantum electrodynamics (QED, the theory underlying classical electrodynamics) the dimensionful elementary electric charge ##e## in coulombs is replaced by the dimensionless charge ##\mathscr{\mathbf{e}}=\frac{e}{\sqrt{\varepsilon_{0}\hbar c}}## and then used to define a dimensionless electric coupling strength ##\alpha_{\text{QED}}\equiv\frac{\mathbf{e}^{2}}{4\pi}=\frac{e^{2}}{4\pi\varepsilon_{0}\hbar c}##. This quantity is usually referred to as the fine-structure "constant", but it actually increases slowly as a function of the energy ##Q## at which it is measured:south said:TL;DR Summary: It's dimensions
Color charge is not scalar. Still, do their components have dimensions (in metrological terms)?
From a theory point of view this is true. However, from a metrological point of view in SI units, electric charge is fundamental and the unit charge is a fundamental defined quantity of measurement. The fine structure constant - or equivalently, ##\epsilon_0## - is of course still a theory parameter to be determined by measurement.renormalize said:Charges and coupling strengths are inherently dimensionless quantities.