Possible confinement mechanisms for nonrelativistic particles on a line

TL;DR

This paper explores confinement mechanisms for nonrelativistic particles on a line within a gauge model that includes nonstandard gravitational and gauge interactions, revealing two distinct confinement types depending on the coupling sign.

Contribution

It introduces a combined gauge and gravitational model, solves for classical and quantum systems analytically, and identifies two confinement mechanisms with potential supersymmetry connections.

Findings

Confinement for positive coupling due to rising potential

Confinement for negative coupling via geometric bag formation

Analytical solutions for energy spectra and supersymmetry relation

Abstract

The gauge model of nonrelativistic particles on a line interacting with nonstandard gravitational fields [5] is supplemented by the addition of a (non)-Abelian gauge interaction. Solving for the gauge fields we obtain equations, in closed form, for a classical two particle system. The corresponding Schr\"{o}dinger equation, obtained by the Moyal quantization procedure, is solved analytically. Its solutions exhibit two different confinement mechanisms - dependent on the sign of the coupling $\lambda$ to the nonstandard gravitational fields. For $\lambda>0$ confinement is due to a rising potential whereas for $\lambda<0$ it is due to to the dynamical (geometric) bag formation. Numerical results for the corresponding energy spectra are given. For a particular relation between two coupling constants the model fits into the scheme of supersymmetrical quantum mechanics.