Chern-Simons Theory & Jones Polynomial
Topological quantum field theory — knot invariants as path integrals
Knot
Trefoil 3₁
Figure-8 4₁
Unknot
Hopf Link
Visualization
Rotation speed:
1.0
Tube thickness:
0.12
CS level k:
4
Jones Polynomial V(t)
V(t) = —
Theory
Z = ∫ DA exp(ik/4π ∫ CS[A])
CS[A] = Tr(A∧dA + ⅔A∧A∧A)
Wilson loop: W_R(γ) = Tr_R P exp∮ A
⟨W⟩ = Jones polynomial V(q)