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MP: Theoretische und Mathematische Grundlagen der Physik

MP V: HV V

MP V.1: Hauptvortrag

Montag, 17. März 1997, 16:25–17:10, HS 133

Singularities of Quantum Fields on Globally and Non-Globally Hyperbolic Spacetimes — •Marek Radzikowski — II. Institut für Theoretische Physik, Universit"at Hamburg

We discuss some of the physical aspects of the ‘wave front set spectral condition’ (WFSSC), which is an equivalent ‘microlocal’ formulation of the global Hadamard condition (GHC) for quasifree states of the Klein-Gordon scalar quantum field theory on a globally hyperbolic curved spacetime (M,g). In particular the WFSSC/GHC [in conjunction with the positivity condition (PC) on the two-point distribution (TPD)] is a necessary condition for the validity of one of Kay’s conjectures: that if the TPD is locally Hadamard, then it must be globally Hadamard. [If there is time we present a simple proof for the case of translation invariant states on Minkowski space. This proof does not require microlocal analysis.]

Also, Kay, Wald, and this speaker have used the Propagation of Singularities Theorem to show that the singularity structure of the (unrenormalized, point-split) stress-energy tensor <T_ab(x,y)> near the Cauchy horizon of a time machine spacetime (a non-globally hyperbolic spacetime) is such that the familiar prescription for finding a renormalized <T_ab(x)> fails to be well-defined. This constitutes perhaps some evidence in support of Hawking’s ‘Chronology Protection Conjecture’.