  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.
