The Strong and Gravitational Couplings of Knotted Solitons

Abstract

We extend our earlier study of the electroweak interactions of quantum knots to their gravitational and strong interactions. The knots are defined by appropriate quantum groups and are intended to describe all knotted field structures that conserve mass and spin, charge and hypercharge, as well as color charge and color hypercharge. As sources of the gravitational fields the knots are described as representations of the quantum group $SL_q(2)$ and as sources of the electroweak and strong fields they are described by $SU_q(2)$. When the point sources of the standard theory are replaced by the quantum knots, the interaction terms of the new Lagrangian density acquire knot form factors and the standard local gauge invariance is supplemented by an additional global $U(1)\times U(1)$ invariance of the $SU_q(2)$ algebra.