Wick Rotation and the Positivity of Energy in Quantum Field Theory

 I shall present joint work with Maxim Kontsevich (arXiv:2105.10161) describing an interesting domain of complex metrics on a smooth manifold. It is a complexification of the space of ordinary Riemannian metrics, and has the Lorentzian metrics (but not metrics of other signatures) on its boundary. By using the domain we are led to a modified axiom system for QFT which illuminates not only the special role of Lorentz signature and the relation of global hyperbolicity to unitarity, but also  other features of QFT such as local commutativity.