4 research outputs found
-Gamma index theorem for spacetimes
No full textWe establish an -Gamma index theorem for the Dirac operator on a globally hyperbolic manifold with Cauchy hypersurface being a Galois covering of a compact smooth manifold with Galois group . Our argument rewrites the -Gamma index in terms of the spectral flow, which is then connected to the usual geometric expressions. This extends the work of Bär and Strohmaier to some non-compact Cauchy hypersurfaces. The analysis here is based on intermediate results by the first author on -Gamma Fredholm properties of the Dirac operator.27 page
Regular singular Sturm–Liouville operators and their zeta-determinants
No full textAbstractWe consider Sturm–Liouville operators on the line segment [0,1] with general regular singular potentials and separated boundary conditions. We establish existence and a formula for the associated zeta-determinant in terms of the Wronski-determinant of a fundamental system of solutions adapted to the boundary conditions. This generalizes the earlier work of the first author, treating general regular singular potentials but only the Dirichlet boundary conditions at the singular end, and the recent results by Kirsten–Loya–Park for general separated boundary conditions but only special regular singular potentials
