Work

Wick rotation in the lapse, admissible complex metrics, and foliation changing diffeomorphisms

Year: 2025

Type: article

Abstract: 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 i ϵ prescription and on Friedmann-Lemaître backgrounds the difference to a Wick rotation in time is illustrated.

Source: Classical and Quantum Gravity

DOI: 10.1088/1361-6382/adc9ef

Authors: Rudrajit Banerjee, Max Niedermaier

Institutions: Okinawa Institute of Science and Technology Graduate University, Centenary College of Louisiana, University of Pittsburgh

Language: English

Topic: Relativity and Gravitational Theory

Subfield: Astronomy and Astrophysics

Field: Physics and Astronomy

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,325

Funders: Agence Nationale de la Recherche, Radboud Universiteit, Centre National de la Recherche Scientifique, Sorbonne Université