  An equality between the spectral flow of a family $A$ of self-adjoint
Fredholm operators and the index of the associated differential operator
$\frac{d}{dt}-iA$ with Atiyah-Patodi-Singer-style boundary conditions is shown.
This generalizes a result by C.B\"ar and A. Strohmaier used to show their
Lorentzian version of the Atiyah-Patodi-Singer Index Theorem.
