Kauffman knot polynomials in classical abelian Chern–Simons field theory

Abstract

Kauffman knot polynomial invariants are discovered in classical abelian Chern–Simons field theory. A topological invariant t I ( L ) is constructed for a link 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.