# Analogy for magnetism in the nuclear strong force?

## Main Question or Discussion Point

Whenever people begin to explain the nuclear strong force, they relate it to electricity. I was wondering if color charges, besides also interacting with one another in a way thats analogous to electricity, can also interact in a way thats analogous to magnetism. I have asked some professors and they said "maybe," but were unfamiliar with it.

## Answers and Replies

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Yes, the strong force involves both "chromoelectricity" and "chromomagnetism." One of the deep insights of special relativity is that electricity and magnetism are two aspects of the same thing, one total electromagnetic field. Similarly there is a chromoelectric field and a chromomagnetic field that are both aspects of one total color field.

Yes, the strong force involves both "chromoelectricity" and "chromomagnetism." One of the deep insights of special relativity is that electricity and magnetism are two aspects of the same thing, one total electromagnetic field. Similarly there is a chromoelectric field and a chromomagnetic field that are both aspects of one total color field.
There are in fact eight of each (though in QFT the 4-potential is most often considered the fundamental fields and the electromagnetic field is considered a derived field.)

Bill_K
Science Advisor
Yes, the strong force involves both "chromoelectricity" and "chromomagnetism."
Do quarks have an anomalous chromomagnetic moment?

There are in fact eight of each (though in QFT the 4-potential is most often considered the fundamental fields and the electromagnetic field is considered a derived field.)
sorry, but eight of what exactly?

And can someone explain how a chromomagnetic field would work if all color-charges must be in bound states?

There are colour effects inherent in descriptions of particle collisions.

See the Lund string model for example. Colour effects are all around at the Lhc where coloured objects are interacting.

Some of these models which include dipole colour interactions are approximations of things we still haven't calculated to high enough accuracy yet.

And these things happen after a collision before these coloured objects form into bound objects(hadronization which occurs at a later time scale)

sorry, but eight of what exactly?
Eight independent set of fields, each equivalent (up to a certain point) to the set of electromagnetic fields.

Do quarks have an anomalous chromomagnetic moment?
I assume so; for example in QCD at one loop you can draw a diagram correcting the quark-quark-gluon vertex that looks exactly like the one-loop QED diagram that corrects the electron-electron-photon vertex and which gives rise to the anomalous magnetic dipole moment of the electron. So at least in perturbation theory you can use that to calculate an anomalous chromomagnetic dipole moment.

That might only work perturbatively, though. In QED you can define the magnetic dipole moment as the derivative of the energy of the one-electron state with respect to the external magnetic field. But in QCD quarks are confined so it's hard to speak of a one-quark state. Maybe nonperturbatively the magnetic dipole moment of a quark is ill-defined?

pantheid said:
And can someone explain how a chromomagnetic field would work if all color-charges must be in bound states?
The fields are also confined; within a proton, say, there is a bundle of quarks all bound together by chromoelectric and chromomagnetic fields. These fields cannot extend far outside the proton, just as the quarks cannot stray outside proton.

Why are you worried about chromomagnetic fields as opposed to chromoelectric fields?

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The fields are also confined; within a proton, say, there is a bundle of quarks all bound together by chromoelectric and chromomagnetic fields. These fields cannot extend far outside the proton, just as the quarks cannot stray outside proton.

Why are you worried about chromomagnetic fields as opposed to chromoelectric fields?[/QUOTE]

I think the question of how they work is pretty interesting, and I want to include some description of it in a paper I'm writing for class.

clem
Science Advisor
Do quarks have an anomalous chromomagnetic moment?
Yes, it leads to a strong spin-spin interaction just like the atomic hyperfine interaction.
This has been known since the start of the quark model, but seems to have been forgotten.