Timeline for Using the covariant derivative to find force between 't Hooft-Polyakov magnetic monopoles
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| Jul 24, 2012 at 10:33 | comment | added | Ron Maimon | @ramanujan_dirac: There is surely no flaw, you just didn't understand it. It is common for people to not understand papers, and make up "flaws" that don't exist (although, as I said, I haven't read it, I know this paper is one of several classics which led to BPS and S-duality). The force between monopoles has been calculated and recalculated again and again, the paper is classic, and it is important in the S-duality of N=4 gauge theory. You just haven't gotten used to reading papers yet, it requires reproducing most of the results yourself. | |
| Jul 24, 2012 at 6:59 | vote | accept | CommunityBot | ||
| Jul 24, 2012 at 6:58 | comment | added | user7757 | Even if this is left out, the paper doesn't make any physical sense to me, and I have not been able to understand the physical essence of the argument, it relies completely on the fact that there should exists some global function defined in a particular way, which should reduce to the versions of these functions each defined independently at each of the monopoles( or anti-monopoles). | |
| Jul 24, 2012 at 6:55 | comment | added | user7757 | apparently there is some flaw in that paper, I have not been completely able to understand it(its related to the smoothness of elliptical functions requiring some functions for the acceleration and gauge fields something like that ) which was pointed out here: prd.aps.org/abstract/PRD/v18/i2/p542_1 | |
| Jul 17, 2012 at 14:42 | comment | added | Ron Maimon | @ramanujan_dirac: In classic papers, it is vanishingly rare that there are typos that substantially affect the result in, but there are occasional minor typos (maybe 1 eqn in 500). But to understand it, you can just pretend that it is full of typos and you are proofreading it. A reseach paper leaves easoning steps that are obvious to the author and referee to the reader, here, it's going back and forth between the time covariant derivative and the time ordinary derivative. This is higher order term in the acceleration, since $A_0$ is infinitesimal for infinitesimal a. | |
| Jul 17, 2012 at 12:22 | comment | added | user7757 | Manton defines $D_\mu \phi = \partial_\mu \phi + e[A_\mu,\phi]$, and $A_0=\epsilon^2 a_i t A_i$, and $\partial_0 \phi = \epsilon^2 a_i t \partial_i \phi $, then how is $D_0 \phi = -\epsilon^2 a_i t D_i \phi$? Is there some resolution to this doubt or is there any typo in the paper (This is the first research paper I have read, so I don't know how common it is to have a typo). | |
| Jul 17, 2012 at 6:07 | comment | added | Ron Maimon | @ramanujan_dirac: I couldn't follow which sign was giving you trouble. I can't access the paper (it's paywalled). It's unfortunate, because it's a classic, and I haven't read it. | |
| Jul 17, 2012 at 5:50 | comment | added | user7757 | Hey, thanks a lot for the answer, but in the definition of covariant derivative he has taken a plus sign, so his covariant derivative is $D_\mu \phi = \partial_\mu \phi+ [A_\mu,\phi]$. See equation 2.3. As regards my comment, I meant I have resolved the sign problem for $D^0 D_0$ where the negative sign disappears because we are taking the contravariant indices. | |
| Jul 17, 2012 at 5:39 | history | answered | Ron Maimon | CC BY-SA 3.0 |