Energy States of Colored Particle in a Chromomagnetic Field

TL;DR

This paper derives the energy states of a colored particle in a constant chromomagnetic field by diagonalizing the Dirac equation, revealing how color interactions split the energy spectrum and establishing supercharge operators for these states.

Contribution

It introduces a unitary transformation to diagonalize the Dirac equation in a chromomagnetic field and constructs supercharge operators ensuring superpartner relationships among energy states.

Findings

Energy states are determined by color interactions with the chromofield.

The spectrum of energy states exhibits splitting due to color interactions.

Supercharge operators are constructed for the diagonalized Hamiltonian.

Abstract

The unitary transformation, which diagonalizes squared Dirac equation in a constant chromomagnetic field is found. Applying this transformation, we find the eigenfunctions of diagonalized Hamiltonian, that describe the states with definite value of energy and call them energy states. It is pointed out that, the energy states are determined by the color interaction term of the particle with the background chromofield and this term is responsible for the splitting of the energy spectrum. We construct supercharge operators for the diagonal Hamiltonian, that ensure the superpartner property of the energy states.