Energy spectrum of simply constant chromoelectric flux tubes

TL;DR

This paper derives the energy spectrum of spinor particles in chromoelectric flux tubes generated by simply constant gauge potentials, revealing discrete spectra with shifts, contrasting classical expectations of continuous acceleration.

Contribution

It introduces a novel analysis of energy spectra in flux tubes from simply constant gauge potentials, differing from the usual covariantly constant case.

Findings

Energy spectrum is discrete due to flux tube walls.

Spectrum has a constant shift depending on the chromoelectric background.

Contrasts classical intuition by showing constant energy eigenvalues.

Abstract

In this article we obtain the energy spectrum of colored, spinor particles in chromoelectric flux tubes. The chromoelectric field of the flux tubes considered here comes from {\em simply} constant gauge potentials rather than from covariantly constant gauge potential, as is usually the case. The energy spectrum of the simply constant flux tubes is different than that of the covariantly constant flux tubes. The spectrum is discrete due to the walls of the tube and with a plus/minus constant shift depending on the magnitude of the constant chromoelectric background. This goes against the classical intuition where one would expect a charged particle in a uniform "electric" field to accelerate with ever increasing velocity/energy i.e. there would be no constant energy eigenvalue.