Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2010-06-08
Annals Phys. 325:2641-2652, 2010
Physics
High Energy Physics
High Energy Physics - Theory
15 pages, 8 figures
Scientific paper
10.1016/j.aop.2010.06.002
Kauffman knot polynomial invariants are discovered in classical abelian Chern-Simons field theory. A topological invariant $t^{I\left( \mathcal{L} \right) }$ is constructed for a link $\mathcal{L}$, where $I$ is the abelian Chern-Simons action and $t$ a formal constant. For oriented knotted vortex lines, $t^{I}$ satisfies the skein relations of the Kauffman R-polynomial; for un-oriented knotted lines, $t^{I}$ satisfies the skein relations of the Kauffman bracket polynomial. As an example the bracket polynomials of trefoil knots are computed, and the Jones polynomial is constructed from the bracket polynomial.
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