Quantum invariants of links and new quantum field models

Abstract

We propose a gauge model of quantum electrodynamics (QED) and its nonabelian generalization from which we derive knot invariants such as the Jones polynomial. Our approach is inspired by the work of Witten who derived knot invariants from quantum field theory based on the Chern-Simon Lagrangian. From our approach we can derive new knot and link invariants which extend the Jones polynomial and give a complete classification of knots and links. From these new knot invariants we have that knots can be completely classified by the power index $m$ of $TrR^{-m}$ where $R$ denotes the $R$-matrix for braiding and is the monodromy of the Knizhnik-Zamolodchikov equation. A classification table of knots can then be formed where prime knots are classified by prime integer $m$ and nonprime knots are classified by nonprime integer $m$.