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My question is in two parts.

  1. What is the origin of the electric field from an electric charge and why electron can have so small mass? While on the other hand for a magnetic monopole to create a magnetic field needs to be so heavy?

  2. And if the magnetic monopole is a hadron what are the constituent elementary particles? What is balancing these energies so that the charges do not explode?

A simple undergrad level answer will do.

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An answer that Professor Lenny Susskind gave to a non-physicist audience at Stanford in June 2012 went along these lines (by memory and some very short notes I took):

The charge on an electron is$\ \alpha \ \approx \ 1/137\ $which means that 99% of the electron is just the bare electron while about 1% of the time it is an electron plus a virtual photon.

Whereas the charge on a magnetic monopole would be $1/\alpha \ \approx \ 137$ so the magnetic monopole would have about 100 constituents on average - like lots of photons, current etc. Thus the magnetic monopole would be a composite particle and very heavy due to all the strong fields and constituents.

Don't blame any errors on Lenny, it could be my mistaken memory/notes. I think that the dimensionless number $\alpha$ is a reasonable stand-in for electric charge since it is the coupling constant used to calculate connections between electrons and photons. Similarly, $1/\alpha$ would be the coupling between magnetic monopoles and photons.

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This is fine, but the large coupling doesn't mean that you get 100 constituents on average. – Ron Maimon Sep 17 '12 at 9:50
@RonMaimon : That is what Lenny said, but remember it was too a large non-physicist audience, so he had to simplify and dumb down for them. By the way, do you know any more about what the constituents might be besides virtual photons? I am pretty sure he said currents but what would that mean? Is a current a virtual e+/e- pair? What other constituents might there be besides photons and virtual charged particle fermion pairs? – FrankH Sep 17 '12 at 11:54
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You can just calculate the energy in the B-field alone. It doesn't get log-screened until the Compton wavelength of the monopole, or the structure scale of the GUT it's a soliton in, whichever is bigger, so you get a large pure electromagnetic mass. This can be thought of as bound virtual photons, but why make life complicated? It's just B^2 energy – Ron Maimon Sep 17 '12 at 19:24
Thanks, Ron. So was Lenny wrong or just exaggerating? – FrankH Sep 17 '12 at 20:06
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He was just taking popularizer's liberty--- you're pretty much allowed to say anything you want in non-internet no-feedback media, since there is no refereeing. He's accurate, but it's a picturesque not so useful way of saying things. Maybe he had something precise in mind, I can't imagine what it is. I think his popular stuff is extremely accurate as far as popular stuff goes. – Ron Maimon Sep 17 '12 at 21:50

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