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