Vortices in He II, current algebras and quantum knots

A canonical quantization scheme is developed for vortices in superfuid He II, using Dirac's technique for constrained hamiltonian systems. Quantization introduces in the theory in a natural way the structure of the infinite Lie algebra of incompressible flows. It is argued that all the topological invariants of the vortex, considered as a knot, can be regarded as observables of the system. Finally unitary representations of measure preserving flows on R3 and current algebra are discussed. (Auth.)