Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
1999-06-04
Int.J.Mod.Phys. A14 (1999) 4347-4363
Physics
High Energy Physics
High Energy Physics - Theory
17 pages, LaTeX2e, no figures, dedicated to Prof. Yu.A. Simonov on the occasion of his 65-th birthday, final published version
Scientific paper
10.1142/S0217751X99002050
In the London limit of the Ginzburg-Landau theory (Abelian Higgs model), vortex dipoles (small vortex loops) are treated as a grand canonical ensemble in the dilute gas approximation. The summation over these objects with the most general rotation- and translation invariant measure of integration over their shapes leads to effective sine-Gordon theories of the dual fields. The representations of the partition functions of both grand canonical ensembles are derived in the form of the integrals over the vortex dipoles and the small vortex loops, respectively. By virtue of these representations, the bilocal correlator of the vortex dipoles (loops) is calculated in the low-energy limit. It is further demonstrated that once the vortex dipoles (loops) are considered as such an ensemble rather than individual ones, the London limit of the Ginzburg-Landau theory (Abelian Higgs model) with external monopoles is equivalent up to the leading order in the inverse UV cutoff to the compact QED in the corresponding dimension with the charge of Cooper pairs changed due to the Debye screening.
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