Abstract
In the framework of geometric quantization, filaments of vorticity in a two-dimensional, ideal incompressible superfluid belong to certain coadjoint orbits of the group of area-preserving diffeomorphisms. The Poisson structure for such vortex strings is analyzed in detail. While the Lie algebra associated with area-preserving diffeomorphisms is noncanonical, we can nevertheless find canonical coordinates and their conjugate momenta that describe these systems. We then introduce a Fock-like space of quantum states for the simplest case of bosonic vortex loops, with natural, nonlocal creation and annihilation operators for the quantized vortex filaments.
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