Abstract
The current algebra arising in the theory of quantum vortices, realized in terms of Chen integrals, is shown to allow the complete reconstruction of the topology of the link supporting the vorticity field, from the equations which impose the condition of flatness for Chen's generalized connection. The conjecture that the set of topological invariants for this link are among the Casimir operators of the current algebra, i.e, are constants of motion of the vortex system, is thus proved. Such invariants correspond to the central elements of the subgroups of the lower central series for the fundamental group of the link. There arises an interesting possibility of an extension towards a generalized Chern-Simons theory.
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