Link Invariants from Classical Chern-Simons Theory

TL;DR

This paper derives explicit, diffeomorphism-invariant link invariants from classical non-Abelian Chern-Simons theory using differential forms, providing a new analytical approach to topological invariants.

Contribution

It introduces a novel method to express link invariants in a diffeomorphism-invariant form via differential forms associated with submanifolds, based on classical Chern-Simons theory.

Findings

Derived analytical expressions for link invariants.

Presented a diffeomorphism-invariant formulation.

Connected link invariants with Abelian gauge symmetry.

Abstract

Taking as starting point a perturbative study of the classical equations of motion of the non-Abelian Chern-Simons Theory with non-dynamical sources, we search for analytical expressions for link invarians. In order to present these expressions in a manifestly diffeomorphism-invariant form, we introduce a set of differential forms associated with submanifolds in Euclidean three-space that allow us to write the link invariants as a kind of surface-dependent diffeomorphism-invariants that present certain Abelian gauge symmetry.