Duality Theory of Strong Interaction

The main objective of this article is to explore the duality of strong interaction based on a new field equations of strong interaction. The field equations are derived by applying the principle of interaction dynamics (PID) and principle of representation invariance (PRI) to a standard QCD SU(3) gauge action functional. Intuitively, PID amounts to taking the variation of the action functional under energy-momentum conservation constraint. PRI requires that physical laws be independent of representations of the gauge groups. The new field equations establish a natural duality between strong gauge fields {Sk μ}, representing the eight gluons, and eight bosonic scalar fields. One prediction of this duality is the existence of a Higgs type bosonic spin-0 particle with mass m ≥ 100GeV/c2. With the duality, we derive three levels of strong interaction potentials: the quark potential Sq , the nucleon/hadron potential Sn and the atom/molecule potential Sa. These potentials clearly demonstrates many features of strong interaction consistent with observations. In particular, these potentials offer a clear mechanism for both quark confinement and asymptotic freedom. Also, in the nuclear level, the new potential is an improvement of the Yukawa potential. As the distance between two nucleons is increasing, the nuclear force corresponding to the nucleon potential Sn behaves as repelling, then attracting, then repelling again and diminishes, consistent with experimental observations. Furthermore, these potentials give rise also to an estimate on the ratio between the gravitational force and the strong interaction force, indicating that near the radius of an atom, the strong repelling force is stronger than the gravitational force, and beyond the molecule radius, the strong repelling force is smaller than the gravitational force. We believe that it is this competition between the gravitational force and the strong force in the level of atoms/molecules that gives rise to the mechanism of the van der Waals force.