by Yablon » Sat Mar 14, 2015 7:05 am
Q-reeus wrote:Jay; while much of your differential forms presentation is outside (i.e. above) my level, I get that there is this flexibility to allow various and independent 'running' of mu (megnetic charge) and e (electric charge). Evidently synonymous with varying and independently variable levels of respective force carrier Boson massiveness (Yukawa-type fields)? But it's not clear to me whether your monopoles now are exclusively or optionally of the original Dirac type (ends of filamentary flux tubes), or 'dressed' 'point particles' thus a true dual of e as per ME's. Could you clarify that matter please? No doubt it is clarified in the paper but on my lazy and low-level read can't quite see where.
Q-reeus:
Let me take a stab at an answer which I hope will be satisfactory. I would have to say that these are monopoles of the original Dirac type, because they are derived from a differential equation which, as one of its solutions, gives the original DQC, and also because I am not using any type of spontaneous symmetry breaking in the manner of 't Hooft, which is what leads to real, observable, topologically stable monopoles which would be a true dual per Maxwell. However, because the original Dirac monopoles asymptotically behave identically to some of the 't Hooft monopole solutions (which depend on the GUT group G and how it is broken down), I would also say that the monopoles I am describing to correspond with the asymptotic behavior of some TP monopoles and so could be true dressed particles. There are several points in the paper which I refer to the asymptotic correspondence, because the point I was trying to bring out (whether I succeeded is another question) is that these could be physical monopoles via a connection to the analysis of 't Hooft. This also makes the GUT arena (eqs. (2.23) to (2.27) and related discussion) a bit tricky because there you presumably can no longer use the asymptotic solution but are getting right on top of the bare particle. In general, a connection to TP is one of the "physical interpretations" that one would engage in,
after totally elaborating the mathematical solutions of the Wu-Yang differential equation. Dirac's two-step is a very good pedagogical approach to always bear in mind. Jay
[quote="Q-reeus"]Jay; while much of your differential forms presentation is outside (i.e. above) my level, I get that there is this flexibility to allow various and independent 'running' of mu (megnetic charge) and e (electric charge). Evidently synonymous with varying and independently variable levels of respective force carrier Boson massiveness (Yukawa-type fields)? But it's not clear to me whether your monopoles now are exclusively or optionally of the original Dirac type (ends of filamentary flux tubes), or 'dressed' 'point particles' thus a true dual of e as per ME's. Could you clarify that matter please? No doubt it is clarified in the paper but on my lazy and low-level read can't quite see where.[/quote]
Q-reeus:
Let me take a stab at an answer which I hope will be satisfactory. I would have to say that these are monopoles of the original Dirac type, because they are derived from a differential equation which, as one of its solutions, gives the original DQC, and also because I am not using any type of spontaneous symmetry breaking in the manner of 't Hooft, which is what leads to real, observable, topologically stable monopoles which would be a true dual per Maxwell. However, because the original Dirac monopoles asymptotically behave identically to some of the 't Hooft monopole solutions (which depend on the GUT group G and how it is broken down), I would also say that the monopoles I am describing to correspond with the asymptotic behavior of some TP monopoles and so could be true dressed particles. There are several points in the paper which I refer to the asymptotic correspondence, because the point I was trying to bring out (whether I succeeded is another question) is that these could be physical monopoles via a connection to the analysis of 't Hooft. This also makes the GUT arena (eqs. (2.23) to (2.27) and related discussion) a bit tricky because there you presumably can no longer use the asymptotic solution but are getting right on top of the bare particle. In general, a connection to TP is one of the "physical interpretations" that one would engage in, [i]after[/i] totally elaborating the mathematical solutions of the Wu-Yang differential equation. Dirac's two-step is a very good pedagogical approach to always bear in mind. Jay
