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I just had a glimpse of the Ginzburg-Landau theory of superconductivity. I am surprised that that the energy of a vortex is finite. This is surprising because as far as I know, in superfluids, the energy of a vortex diverges logarithmically with the size of the system.

Is it because of the coupling to the EM field? In a superfluid, the divergence comes form the kinetic energy. In a superconductor, the kinetic term is modified by including the vector potential, so that decreases the kinetic energy?

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    $\begingroup$ It is indeed true, that the reason is the coupling to a gauge field. The matter at hand is described in detail in "Topological Solitons" by N. Manton and P. Sutcliffe (In the version of 2004 you find the discussion on pages 158 - 165). $\endgroup$ May 5 at 8:55

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