Kauffman knot polynomials in classical abelian Chern–Simons field theory

Kauffman knot polynomial invariants are discovered in classical abelian Chern–Simons field theory. A topological invariant tI(L)tI(L) is constructed for a link LL, where I is the abelian Chern–Simons action and t a formal constant. For oriented knotted vortex lines, tI satisfies the skein relations of the Kauffman R-polynomial; for un-oriented knotted lines, tI 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.