Talk:Order-disorder

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This article is very confusing. I thought that there are no topological sectors for a pure scalar theory in 3+1 dimensions because the solitons are infinitely massive. Unless the person who wrote this article had the Higgs mechanism in mind. But that can't be it, because massless Goldstone bosons are mentioned. QFT 14:31, 15 December 2005 (UTC)

The article is confusing, but the argument is really interesting. It's got a nice analogy between the phenomenon of charges in the vaccuum in Higgsing, and the phenomenon of fluctuations zeroing out the average field. About the point that you raise--- the topological sectors. There are no finite energy sectors, but they don't have to be finite energy. You can just stuff an infinite energy configuration and look at small fluctuations about it. In particular, the center of the topological defect can still move around even if the total energy is infinite if the difference in energy between two centers is finite.

Same is true in SU(2) for example, if you unhiggs it. Then the SU(2) confines and the nontrivial reps are all infinite energy in the same way. So they have a string stretching out to infinity. I'm not sure if the center can move in either case, but its still a vaccuum selection principle.

I rewrote the article to be clearer. Hope the original author doesn't get offended. I think there was one mistake--- the Z₂ symmetry from the SO(3) isn't necessary at all, and just makes things murky. Likebox 02:54, 19 September 2007 (UTC)