About the non-standard viewpoint on the dynamics of closed vortex filament

TL;DR

This paper develops a Hamiltonian framework for closed vortex filament dynamics using non-standard variables, revealing a quasiparticle interpretation with Galilei invariance and providing an explicit effective mass formula.

Contribution

It introduces a novel Hamiltonian description with non-standard variables and constraints, offering a new perspective on vortex filament energy and effective mass.

Findings

System described as a quasiparticle with internal and external degrees of freedom

Hamiltonian formulation invariant under Galilei group

Explicit formula for the effective mass of the vortex filament

Abstract

In this article we construct the Hamiltonian description of the closed vortex filament dynamics in terms of non-standard variables, phase space and constraints. The suggested approach makes obvious interpretation of considered system as a quasiparticle that possess certain external and internal degrees of the freedom. The constructed theory is invariant under the transformation of Galilei group. The appearance of this group allows for a new viewpoint on the energy of a closed vortex filament with zero thickness. The explicit formula for the effective mass of the quasiparticle 'closed vortex filament' is suggested.