Science behind magnetic monopoles in any depth?

[Just some guy]

Hi,

Just wondering, does anybody know of any texts or websites that go into the science behind magnetic monopoles in any depth? I'm thinking of writing a report on them as part of my A2 course but I can't find much information about them! (apart from the fact that nobody's detected them and people think they might not exist, but what the heck )

 

[quasar987]

The existence of magnetic monopoe would be very fun because it would explain quantization of charge (i.e. why charges come in integer multiples of e) and also because it would make the Maxwell equations more symetrical. They would become (in Gaussian units)

$$\nabla \cdot \vec{E} = \rho_e$$
$$\nabla \cdot \vec{B} = \rho_m$$
$$\nabla \times \vec{E} = -\vec{J}_m- \frac{\partial \vec{B}}{\partial t}$$
$$\nabla \times \vec{B} = \vec{J}_e+\frac{\partial \vec{E}}{\partial t}$$


Read the wiki page if you haven't: http://en.wikipedia.org/wiki/Magnetic_monopoles

 

[Just some guy]

Yes, I've read the wiki article, but it isn't really enough to base a 4000 word report on...

 

[quasar987]

4000 words that's a lot, I'll agree.

And the equations I wrote are probably wrong in the units area; there should be a bunch of 4pi and c I think... sorry bout that.

 

[masudr]

Study the maxwell's generalised equations. Look up duality transformations, look up one-forms, hodge duals. Believe me there's way more than 4000 words to write on this. However a lot of this stuff might be tough for A2; are you doing the Advancing Physics (IoP) course?

 

[masudr]

And the equations I wrote are probably wrong in the units area; there should be a bunch of 4pi and c I think... sorry bout that.

If we have the electric current density 4-vector $\rho^e=(-\rho^e/c, j_x^e, j_y^e, j_z^e)$ (sorry about the bad notation), then the magnetic current density 4-vector would be (I think) $\rho^m=(\rho^m, j^m_x/c, j^m_y/c, j^m_z/c)$ (where both are written as covariant vectors).

Could someone correct me if I'm wrong? (I suppose I should just check the units...)

 

[Just some guy]

Study the maxwell's generalised equations. Look up duality transformations, look up one-forms, hodge duals. Believe me there's way more than 4000 words to write on this. However a lot of this stuff might be tough for A2; are you doing the Advancing Physics (IoP) course?

Yes I am. I know it might be a bit beyond me but I want to do something exceptional and I'm willing to try some of the more advanced stuff. Thanks for the advice

 

[samalkhaiat]

Yes I am. I know it might be a bit beyond me but I want to do something exceptional and I'm willing to try some of the more advanced stuff.

OK, TRY THESE;

1. DIRAC, THE MONOPOLE CONCEPT, INTR.JOUR.THRO.PHYS,V17,No4(1978)
2. KAZAMA, ELECTRON-MONOPOLE SYSTEM, AS ABOVE PP249-265
3. BRANDT & PRIMACK, DYONS, AS ABOVE,PP267-273
4. MARCIANO, NON-ABELIAN MONOPOLES, AS ABOVE,PP275-286
5. NAMBU, TOPOLOGICAL CONFIG IN GAUGE THEORIES, AS ABOVE,PP287-292
6. FREUND, MONOPOLES,TOPOLOGY,SYMMETRY, AS ABOVE,PP301-308.
7.RAJARAMAN, SOLITONS & INSTANTONS, NORTH HOLLAND PRESS.1982
REFERENCE No7 IS A 400 PAGE BOOK.



REGARDS

sam

 

[masudr]

Yes I am. I know it might be a bit beyond me but I want to do something exceptional and I'm willing to try some of the more advanced stuff. Thanks for the advice

I did the same A-Level course as you in the years 2002-2004. For my A2 research report, I zoomed over the 3 problems that classical mech + electrodynamics could not explain, I did a brief review on the mathematics of linear vector spaces (and operators defined on them), and then went on to the postulates of quantum mechanics, a list of some operators in position representation, and as an example I solved the particle in a 1D box problem.

Obviously I was about 2 years ahead in terms of when people normally learn QM, and so undoubtedly there were some oversights (or errors if you like) in my work, but it did not fit in very well the criteria on the mark scheme, since I did not have many diagrams etc; in fact apart from the graphs of the wavefunctions I had no diagrams! So my teacher could not give me any more than 32/40 marks (which was an A) but I felt it perhaps deserved more.

While monopoles are interesting, the best way to look at them would be in covariant equations, and that requires learning about tensors, component notation, lorentz transformations as a (1, 1) tensor, and 4-vectors and such like. While you probably could learn it all, I don't think you'd have the time. I recommend you find a more well-documented phenomenon, especially one that can have a lot of good pictures etc. I think that examinations are ridiculous, and are designed to get you to jump through hoops. It's slightly different here as an undergrad at Oxford, but A-Levels (and much more so GCSEs) are a lot to do with hoop-jumping.

Hope this helps.

 

[Just some guy]

OK, TRY THESE;
1. DIRAC, THE MONOPOLE CONCEPT, INTR.JOUR.THRO.PHYS,V17,No4(1978)
2. KAZAMA, ELECTRON-MONOPOLE SYSTEM, AS ABOVE PP249-265
3. BRANDT & PRIMACK, DYONS, AS ABOVE,PP267-273
4. MARCIANO, NON-ABELIAN MONOPOLES, AS ABOVE,PP275-286
5. NAMBU, TOPOLOGICAL CONFIG IN GAUGE THEORIES, AS ABOVE,PP287-292
6. FREUND, MONOPOLES,TOPOLOGY,SYMMETRY, AS ABOVE,PP301-308.
7.RAJARAMAN, SOLITONS & INSTANTONS, NORTH HOLLAND PRESS.1982
REFERENCE No7 IS A 400 PAGE BOOK.
REGARDS
sam

Hmm, I can't find 'the monopole concept' anywhere - is it still in print and if so where can I get it from?

 

[masudr]

Hmm, I can't find 'the monopole concept' anywhere - is it still in print and if so where can I get it from?

It's a journal, not a book. Look in a big academic library, or look up the journal online.