Relation between confinement and higher symmetry restrictions for color particle motion

TL;DR

This paper explores how higher symmetry restrictions in quantum phase space, specifically O(2,6) invariance, lead to an oscillator potential that models the confinement of color particles like quarks.

Contribution

It introduces a framework linking confinement to higher symmetry restrictions in quantum phase space using the Snyder-Yang algebra.

Findings

Derived an equation of motion with an oscillator potential for color particles.

Estimated the oscillator parameter and related it to quark masses.

Showed confinement can be simulated through symmetry-induced potentials.

Abstract

Quantum operators of coordinates and momentum components of a particle in the Minkowski spacetime can belong to the generalized Snyder-Yang algebra and produce a quantum phase space with three new constants in the general case. With account for the O(2,6) invariance in the quantum phase space of a color particle the equation of motion is obtained, which contains a oscillator rising potential. The presence of the oscillator potential can simulate a confinement of a color particle. A parameter of the oscillator potential is estimated and a relationship between current and constituent quark masses is obtained.