  We derive a hydrodynamic model for a liquid of arbitrarily curved flux-lines
and vortex loops using the mapping of the vortex liquid onto a liquid of
relativistic charged quantum bosons in 2+1 dimensions recently suggested by
Tesanovic and by Sudbo and collaborators. The loops in the flux-line system
correspond to particle-antiparticle fluctuations in the bosons. We explicitly
incorporate the externally applied magnetic field which in the boson model
corresponds to a chemical potential associated with the conserved charge
density of the bosons. We propose this model as a convenient and physically
appealing starting point for studying the properties of the vortex liquid.
