Physics – Condensed Matter – Mesoscale and Nanoscale Physics
Scientific paper
2002-08-28
J.Phys.A35:8859-8866,2002
Physics
Condensed Matter
Mesoscale and Nanoscale Physics
To appear in Journal of Physics A
Scientific paper
10.1088/0305-4470/35/41/316
The kinetic part of the Rasetti-Regge action I_{RR} for vortex lines is studied and links to string theory are made. It is shown that both I_{RR} and the Polyakov string action I_{Pol} can be constructed with the same field X^mu. Unlike I_{NG}, however, I_{RR} describes a Schwarz-type topological quantum field theory. Using generators of classical Lie algebras, I_{RR} is generalized to higher dimensions. In all dimensions, the momentum 1-form P constructed from the canonical momentum for the vortex belongs to the first cohomology class H^1(M,R^m) of the worldsheet M swept-out by the vortex line. The dynamics of the vortex line thus depend directly on the topology of M. For a vortex ring, the equations of motion reduce to the Serret-Frenet equations in R^3, and in higher dimensions they reduce to the Maurer-Cartan equations for so(m).
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