Quantum Knots and New Quantum Field Theory

Abstract

We propose a new gauge theory of quantum electrodynamics (QED) and quantum chromodynamics (QCD) 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 invariants which extend the Jones polynomial and give a complete classification of knots. We model elementary particles by quantum knots. From the construction of quantum knots we construct quantum photon propagator and quantum gloun propagator for the nuclear force beween elementary particles. Then from the propagators a renormalization group equation is derived for the critical phenomena of QED and QCD of electrons and quarks including superconductivity and color superconductivity.