Speaker
Description
A Wick rotation in the lapse (not in time) is
introduced for all foliated metric geometries that leads to
admissible complex metrics dampening the exponential of the action.
Starting from a Euclidean signature scalar field FRG a well-defined
Wick rotated version arises that covers the near Lorentzian
regime. Augmenting the mathematical toolbox, a near Lorentzian
counterpart of the heat kernel is rigorously constructed along
these lines, whose asymptotic expansion allows one to control
the ultraviolet aspects of the FRG solutions for strictly
Lorentzian signature. The asymptotic expansion of the
Wick rotated heat kernel induces the Hadamard parametrix for
the Green's function associated with it via Laplace transform.
However, not all physically relevant Green's functions arise
in this way. A perspective on a stand-alone Green's function
variant of the formalism is outlined for Bianchi I cosmological
backgrounds.
