Solitonic Aspects of q-Field Theories

TL;DR

This paper explores how deforming non-Abelian gauge theories with quantum groups introduces new degrees of freedom, leading to solitonic particles that may represent quark-like constituents, revealing non-locality and dual algebra structures.

Contribution

It introduces a novel interpretation of q-deformed gauge theories, linking additional degrees of freedom to non-locality and dual algebra structures, with specific analysis of q-deformed SU(2) and GL_q(3).

Findings

Deformed gauge theories have more degrees of freedom than original theories.

New algebraic structures emerge, with one approaching the original Lie algebra in a limit.

Exotic particles may serve as quark-like constituents of solitons.

Abstract

We have examined the deformation of a generic non-Abelian gauge theory obtained by replacing its Lie group by the corresponding quantum group. This deformed gauge theory has more degrees of freedom than the theory from which it is derived. By going over from point particles in the standard theory to solitonic particles in the deformed theory, it is proposed to interpret the new degrees of fredom as descriptive of a non-locality of the deformed theory. It also turns out that the original Lie algebra gets replaced by two dual algebras, one of which lies close to and approaches the original Lie algebra in a correspondence limit, while the second algebra is new and disappears in this same correspondence limit. The exotic field particles associated with the second algebra can be interpreted as quark-like constituents of the solitons, which are themselves described as point particles in the first algebra. These ideas are explored for q-deformed SU(2) and $GL_q(3)$.