2024/06/10 by Rudrajit Banerjee, Banerjee, Rudrajit, M. Niedermaier +1 · 2 citations
Engineering · #Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #Granular flow and fluidized beds #Heat Transfer Mechanisms #Heat and Mass Transfer in Porous Media #High Energy Physics - Theory (hep-th) #Mathematical Physics (math-ph)
paper · pdf · doi:10.48550/arxiv.2406.06047
openalex publication_date 2024/06/10 · openalex created_date 2024/06/12 · openalex updated_date 2026/08/01
A Wick rotation in the lapse (not in time) is introduced that interpolates between Riemannian and Lorentzian metrics on real manifolds admitting a codimension-one foliation. The definition refers to a fiducial foliation but covariance under foliation changing diffeomorphisms can be rendered explicit in a reformulation as a rank one perturbation. Applied to scalar field theories a Lorentzian signature action develops a positive imaginary part thereby identifying the underlying complex metric as ``admissible''. This admissibility is ensured in non-fiducial foliations in technically distinct ways also for the variation with respect to the metric and for the Hessian. The Hessian of the Wick rotated action is a complex combination of a generalized Laplacian and a d'Alembertian, which is shown to have spectrum contained in a wedge of the upper complex half plane. Specialized to near Minkowski space the induced propagator differs from the one with the Feynman iε prescription and on Friedmann-Lemaître backgrounds the difference to a Wick rotation in time is illustrated.