  The spectrum of the two-dimensional continuum Dirac operator in the presence
of a uniform background magnetic field consists of Landau levels, which are
degenerate and separated by gaps. On the lattice the Landau levels are spread
out by discretization artefacts, but a remnant of their structure is clearly
visible (Hofstadter butterfly). If one switches on a non-Abelian interaction,
the butterfly structure will be smeared out, but the lowest Landau level (LLL)
will still be separated by a gap from the rest of the spectrum. In this talk we
discuss how one can define the LLL in QCD and check how well certain physical
quantities are approximated by taking into account only the LLL.
