Seminario di David O'Connell (OIST)

In this talk I will overview an ongoing project which revolves around the problem of defining QFTs on a non-Hausdorff spacetime. After a brief review of the locally-covariant formalism for QFT on curved spacetimes, we will spend some time understanding the “adjunction formalism” of non-Hausdorff differential geometry. In particular, we will see that ordinary globally-hyperbolic spacetimes can be “glued together” in order to describe non-Hausdorff spacetimes that exhibit topology change. Interestingly, this is in stark contrast to the usual version of topology change: in the non-Hausdorff case, our spacetime will be covered by a preferred set of globally-hyperbolic (Hausdorff) submanifolds, which doesn’t happen in the Hausdorff case. Once this observation is understood, we will see that the formalism of non-Hausdorff geometry seems to naturally cohere with locally covariant QFT: the QFTs on a non-Hausdorff spacetime can be described by “gluing together” QFTs defined on maximal globally-hyperbolic Hausdorff submanifolds. Time permitting, we will finish with an example of the Klein-Gordon field on a non-Hausdorff background, as well as some interesting observations for the near-future.