Simon Scott

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 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 decompositionS1=X0∪X1, we explain how the determinant of a Dirac-type operator overS1 is related to the determinants of the corresponding boundary value problems overX0 andX1.

The

Abstract. Let

\zeta

{\cal D}

-determinant and Quillen determinant for a Dirac operator on a manifold with boundary

denote a Dirac operator on a compact odd-dimensional manifold M with boundary Y. The elliptic boundary value problem

The Residue Determinant

{\cal D}_P

Traces and determinants of pseudodifferential operators

is the operator

Splitting the curvature of the determinant line bundle

{\cal D}

ζ-determinant and the Quillen determinant on the Grassmannian of elliptic self-adjoint boundary conditions

with domain determined by a boundary condition P from the smooth self-adjoint Grassmannian

Functorial QFT, Gauge Anomalies¶and the Dirac Determinant Bundle

Gr^*_{\infty}({\cal D})

Determinants, Grassmanniannians and Elliptic Boundary Problems for the Dirac Operator

. It has a well-defined