SL_q(3) Fields

TL;DR

This paper extends the construction of q-field theories from SU_q(2) to SL_q(3), revealing a dual-sector structure with standard and hypothetical, hard-to-detect particles, including quark-like and gluon-like entities.

Contribution

It introduces a new SL_q(3) q-field theory, expanding previous work on SU_q(2) and exploring the properties of two distinct particle sectors.

Findings

Two sectors: standard and invisible particles

Hypothetical particles include quark-like and gluon-like entities

Second sector particles are difficult to detect and vanish at q=1

Abstract

The q-field theories are constructed by substituting quantum groups for the usual Lie groups. In earlier papers this construction was carried out for the quantum group SU_q(2). Here the investigation is extended to SL_q(3). The resulting theory describes two sectors, one sector lying close to the standard theory and accessible by perturbation theory, while the second sector describes particles that should be difficult to detect and become invisible in the q=1 limit. In this note we discuss these hypothetical particles: three quark-like spinor particles coupled to three gluon-like vector particles.