The Identification and Properties of Linked and Knotted flux tubes in Particle Physics

Abstract

This thesis summarizes the research I have done during my graduate tenure at Vanderbilt University. The core of the thesis is a model of glueballs as tightly knotted or linked chromoelectric flux tubes. The model is based on a direct relationship between the mass of a glueball state and the energy of a knot or link. A particular knot or link is identified with a glueball ground state, and the excited states are modeled as rotational excitations. The rotational energy was first calculated based on an approximate spherical symmetry and then later generalized to take into consideration the true symmetry of each knot and link used in the model. The moment of inertia tensor was computed in order to properly categorize the knots and links. The moment of inertia tensor was calculated exactly for several chain links and generalized for a link with 'n' elements; the remaining calculations were based on sets of vertex coordinate points.