Spectral geometry of spacetime

Abstract

Spacetime, understood as a globally hyperbolic manifold, may be characterized by spectral data using a 3+1 splitting into space and time, a description of space by spectral triples and by employing causal relationships, as proposed earlier. Here, it is proposed to use the Hadamard condition of quantum field theory as a smoothness principle.Comment: AMS-LaTeX, 6 pages,Talk presented at the Euroconference on "Non-Commutative Geometry And Hopf Algebras In Field Theory And Particle Physics" Torino, Villa Gualino, September 20 - 30, 199