In contrast to the Riemannian case, the Dirac operator D on a Lorentzian spin manifold is not formally self-adjoint in the usual sense. Nevertheless, it turns out that if the manifold is asymptotically Minkowski, D^2 has real spectrum apart possibly from some complex resonances. Moreover, we show that D has a well-defined spectral zeta function density, the poles of which are geometric invariants. The proof involves new microlocal estimates in the asymptotically flat setting when the spectral parameter has large imaginary part. (joint work with N. V. Dang and A. Vasy)
Romain Duboscq, David Lafontaine
