Dual transformation in Abelian gauge theories

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Abstract
The dual transformation discovered in the two-dimensional Ising and planar Heisenberg models is applied to gauge theories in four dimensions. It is shown that after the dual transformation the Abelian Higgs model gives the same partition function as the relativistic hydrodynamics of Kalb and Ramond and of Nambu coupled to the Higgs scalar, and that these two theories have various dual relations. In our hydrodynamics a quantized vortex is created by the phase component of the Higgs scalar in a similar manner as the magnetic string of Nielsen and Olesen is created in the Abelian Higgs model.