Abstract
We consider the transverse force on a moving vortex with the acoustic metric using the φ-mapping topological current theory. In the frame of effective space–time geometry the vortex appear naturally by virtue of the vortex tensor in the Lorentz space–time and we show that it is just the vortex derived with the order parameter in the condensed matter. With the usual Lagrangian we obtain the equation of motion for the vortex. At last, we show that the transverse force on the moving vortex in our equation is just the usual Magnus force in a simple model.
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