On the Pairing Structure of the Vacuum induced by a Magnetic Field in 2+1-dimensional Dirac Field Theory

TL;DR

This paper derives an exact expression for the vacuum state of a 2+1D Dirac field in a magnetic field, revealing a unique two-level pairing structure and clarifying the condensate's nature in the lowest Landau level.

Contribution

It provides an exact vacuum state expression using Bogoliubov transformations, highlighting a novel pairing structure in the presence of a magnetic field.

Findings

Reveals a two-level pairing structure in the vacuum

Clarifies the nature of the condensate in the lowest Landau level

Provides an exact expression for the vacuum state

Abstract

Using a sequence of Bogoliubov transformations, we obtain an exact expression for the vacuum state of a Dirac field in 2+1 dimensions in presence of a constant magnetic field. This expression reveals a peculiar two level pairing structure for any value of the mass m greater than zero. This calculation clarifies the nature of the condensate in the lowest Landau level whose existence has been emphasized recently by a several authors.