  An alternative approach to the derivation of the force on a vortex based in
an adiabatic approximation in the action of the superfluid system is developed.
Assuming that the vortex motion is relatively slow compared with the
characteristic times involved in the microscopic degrees of freedom, the effect
of the superfluid and its excitations is reduced to a gauge potential, and the
associated transverse force. The vortex velocity part of the transverse force
is found in terms of the thermal expectation of the angular momentum of the
fluid around the vortex. The excitations countercirculate the vortex reducing
the effective density to that of the superfluid part only.
  Non-adiabatic contributions appear in this formalism as a non-Abelian gauge
potential connecting different microscopic states, in particular the
renormalization of the vortex mass is given by the lowest order diagonal
correction to the adiabatic theory, and the long wavelength contributions found
to depend only on the static structure factor for the fluid.
