Landau levels in QCD in an external magnetic field

TL;DR

This paper investigates Landau levels of quarks in lattice QCD under an external magnetic field, establishing a method to identify the lowest Landau level in both 2D and 4D cases, aiding the validation of low-energy QCD models.

Contribution

It introduces a way to define and identify the lowest Landau level in four-dimensional lattice QCD with magnetic fields, extending previous 2D results.

Findings

Lowest Landau level can be unambiguously identified in 2D with interactions.

A method to define the lowest Landau level in 4D QCD is proposed.

Results help test the validity of low-energy QCD models using the lowest-Landau-level approximation.

Abstract

We will discuss the issue of Landau levels of quarks in lattice QCD in an external magnetic field. We will show that in the two-dimensional case the lowest Landau level can be identified unambiguously even if the strong interactions are turned on. Starting from this observation, we will then show how one can define a "lowest Landau level" in the four-dimensional case, and discuss how much of the observed effects of a magnetic field can be explained in terms of it. Our results can be used to test the validity of low-energy models of QCD that make use of the lowest-Landau-level approximation.