  Functional determinants for Dirac operators on manifolds with boundary are
considered. Ellipticity of boundary value problems is discussed in terms of the
Calderon projector.
  The functional determinant for a Dirac operator on a bidimensional disk, in
the presence of an Abelian gauge field, subject to global boundary conditions
of the type introduced by Atiyah-Patodi-Singer, is evaluated. The relationship
with the index theorem is also commented.
