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.
All Science Journal Classification (ASJC) codes
- Statistical and Nonlinear Physics
- Mathematical Physics