Motion of quantized vortices as elementary objects

The general local, nondissipative equations of motion for a quantized vorte x moving in an uncharged laboratory superfluid are derived from a relativis tic, co-ordinate invariant Framework having vortices as its elementary obje cts in the form of stable topological excitations. This derivation is carri ed out for a pure superfluid with all isotropic gap at the absolute zero of temperature, on the level of a hydrodynamic, collective co-ordinate descri ption. In the formalism, we use as fundamental ingredients that particle nu mber as well as vorticity are conserved and that the fluid is perfect. No a ssumptions are involved as regards the dynamical behaviour of the order par ameter. The interaction of the vortex with the background fluid, representi ng the Magnus force, and with itself via phonons, giving rise to the hydrod ynamic vortex mass, are separated. For a description of the motion of the v ol tex in a dense laboratory superfluid such as helium III two limits have to be considered: The nonrelativistic limit for the superfluid background i s taken, and the motion of the vortex is restricted to velocities much less than the speed of sound. The canonical structure of vortex motion in terms of the collective co-ordinate is used for the quantization of this motion. (C) 1999 Academic Press.