We examine the kinematics of quantum vortex configurations in three-dimensional space for an ideal incompressible fluid. The permitted quantum configurations are shown to be surfaces of vorticity, characterized topologically not only by their knottedness, but also by additional global properties such as twists and holes. Our results, obtained by representing an infinite-dimensional group of diffeomorphisms, contradict conclusions reached by approximating the infinite-dimensional system with finitely many degrees of freedom.
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Goldin et al. (1991) studied this question.
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