DETERMINANTS OF DIRAC BOUNDARY-VALUE-PROBLEMS OVER ODD-DIMENSIONAL MANIFOLDS

We present a canonical construction of the determinant of an elliptic selfadjoint boundary value problem for the Dirac operator D over an od d-dimensional manifold. For 1-dimensional manifolds we prove that this coincides with the zeta-function determinant. This is based on a resu lt that elliptic self-adjoint boundary conditions for D are parameteri zed by a preferred class of unitary isomorphisms between the spaces of boundary chiral spinor fields. With respect to a decomposition S-1 = X(0) boolean OR X(1), we explain how the determinant of a Dirac-type o perator over S-1 is related to the determinants of the corresponding b oundary value problems over X(0) and X(1).