  We consider a relativistic two-fluid model of superfluidity, in which the
superfluid is described by an order parameter that is a complex scalar field
satisfying the nonlinear Klein-Gordon equation (NLKG). The coupling to the
normal fluid is introduced via a covariant current-current interaction, which
results in the addition of an effective potential, whose imaginary part
describes particle transfer between superfluid and normal fluid. Quantized
vorticity arises in a class of singular solutions and the related vortex
dynamics is incorporated in the modified NLKG, facilitating numerical analysis
which is usually very complicated in the phenomenology of vortex filaments. The
dual transformation to a string theory description (Kalb-Ramond) of quantum
vorticity, the Magnus force and the mutual friction between quantized vortices
and normal fluid are also studied.
