An index theorem for Lorentzian manifolds

We prove an index theorem for the Dirac operator on compact
Lorentzian manifolds with spacelike boundary. Unlike in the
Riemannian situation, the Dirac operator is not elliptic. But
it turns out that under Atiyah-Patodi-Singer boundary conditions,
the kernel is finite dimensional and consists of smooth sections.
The corresponding index can be expressed by a curvature integral,
a boundary transgression integral and the eta-invariant of the
boundary just as in the Riemannian case. There is a natural physical
interpretation in terms of particle-antiparticle creation. This is
joint work with Alexander Strohmaier.