Abstract: The Tomita-Takesaki theory of modular automorphisms has found many uses in quantum field theory, in particular in computing relative entropies. However, the modular Hamiltonian is only known in some cases. I present results for the full modular data (flow, Hamiltonian and involution) for conformal scalar fields in the de Sitter (Bunch-Davies) vacuum state, restricted to diamonds. I further show that in the limit where the diamonds become large and fill the full static patch, the modular Hamiltonian generates time translations in the static patch, recovering the results of Sewell and Kay for this case.

Abstract: The heat kernel is a central object for quantum field theory in Euclidean signature, both for one-loop perturbation theory and non-perturbative functional renormalization group methods. On generic curved backgrounds, however, the link between Euclidean and Lorentzian signature QFT via a Wick rotation is not fully understood. In this talk I will present a proposal for Wick rotating on generic globally hyperbolic manifolds by analytically continuing the lapse function in the ADM decomposition. This keeps the coordinates real and can be shown to define “admissible” complex metrics even under foliation changing diffeomorphisms.  A proof of existence of the associated Wick-rotated heat semi-group (and its kernel) will be sketched, together with a conjecture on the strict Lorentzian limit. Some aspects are illustrated with the Wick rotated deSitter heat kernel.