The Strong and Gravitational Couplings of Knotted Solitons

TL;DR

This paper explores how quantum knots, modeled by quantum groups, can serve as sources for gravitational, electroweak, and strong interactions, extending previous work to include gravitational and strong couplings.

Contribution

It introduces a framework where quantum knots are described by specific quantum groups and act as sources for multiple fundamental interactions, incorporating new gauge invariance features.

Findings

Quantum knots are modeled as representations of $SL_q(2)$ and $SU_q(2)$.

Interaction terms gain knot-specific form factors.

Standard gauge invariance is extended by a global $U(1) imes U(1)$ symmetry.

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.