Abstract
We present a canonical construction of the determinant of an elliptic selfadjoint boundary value problem for the Dirac operatorD over an odd-dimensional manifold. For 1-dimensional manifolds we prove that this coincides with the ζ-function determinant. This is based on a result that elliptic self-adjoint boundary conditions forD are parameterized by a preferred class of unitary isomorphisms between the spaces of boundary chiral spinor fields. With respect to a decompositionS 1=X 0∪X 1, we explain how the determinant of a Dirac-type operator overS 1 is related to the determinants of the corresponding boundary value problems overX 0 andX 1.
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