A microscopic theory of vortices in superfluid helium

It is shown that the introduction of the depletion velocity field, the vortical part of the fluid velocity, is rooted on the nature of the field operators. This result is obtained by formulating the theory of vortices in terms of the vortex coordinates. The modified Hamilton-Jacobi equation leads to a generalization of the Schrödinger equation for a particle in the presence of a vortex line. It is shown that our theory is intimately related to the microscopic theory of Bose systems developed by Nishiyama. Mention is made of the close relation between the Higgs mechanism and a gauge-wheel in superfluid helium.