Knot polynomial invariants in classical Abelian Chern-Simons field theory

Xin Liu

doi:10.1016/j.aop.2010.06.002

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arXiv · 1006.1675

Knot polynomial invariants in classical Abelian Chern-Simons field theory

Xin Liu

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Abstract

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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Xin Liu. 2010-06-08. Knot polynomial invariants in classical Abelian Chern-Simons field theory. https://doi.org/10.1016/j.aop.2010.06.002

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