Quantum Kinematics of Bosonic Vortex Loops

摘要

Poisson structure for vortex filaments (loops and arcs) in 2D ideal211u001eincompressible fluid is analyzed in detail. Canonical coordinates and momenta on 211u001ecoadjoint orbits of the area-preserving diffeomorphism group, associated with 211u001esuch vortices, are found. The quantum space of states in the simplest case of 211u001ebosonic vortex loops is built within a geometric quantization approach to the 211u001edescription of a quantum fluid. Fock-like structure and non-local creation and 211u001eannihilation operators of quantum vortex filaments are introduced.