On the pairing structure of the vacuum induced by a magnetic field in 2+1-dimensional Dirac field theory

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≥0. This calculation clarifies the nature of the condensate in the lowest Landau level whose existence has been emphasized recently by several authors.