Quantization of vortices in 4He and lambda-transition

An attempt to give a theoretical explanation of the Λ -transition in liquid 4He is made in terms of quantum statistical mechanics. A canonical quantization scheme is developed for vortices in superfluid He 2, taking as a starting point the classical Thompson theory of vortices. The next step is made for realizing that the structure of a current algebra A and of the corresponding group generate a space of configurations which is more similar to a set of planar Jordan curves, than to a set of three-dimensional loops. Such unexpected feature stems out of the explicit construction of a complete set of commuting observables from the generators of the algebra A. The final step of the theory is computing the grand-canonical partition function