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This content will become publicly available on March 1, 2026

Title: On the lapse contour in the gravitational path integral
The gravitational path integral is usually implemented with a covariant action by analogy with other gauge field theories, but the gravitational case is different in important ways. A key difference is that the integrand has an essential singularity, which occurs at zero lapse where the spacetime metric degenerates. The lapse integration contour required to impose the local time reparametrization constraints must run from to + , yet must not pass through zero. This raises the question: for an application—such as a partition function—where the constraints should be imposed, what is the correct integration contour, and why? We study that question by starting with the reduced phase space path integral, which involves no essential singularity. We observe that if the momenta are to be integrated before the lapse, to obtain a configuration space path integral, the lapse contour should pass below the origin in the complex lapse plane. This contour is also consistent with the requirement that quantum field fluctuation amplitudes have the usual short distance vacuum form, and with obtaining the Bekenstein-Hawking horizon entropy from a Lorentzian path integral. Published by the American Physical Society2025  more » « less
Award ID(s):
2309634
PAR ID:
10614418
Author(s) / Creator(s):
;
Publisher / Repository:
Physical Review D
Date Published:
Journal Name:
Physical Review D
Volume:
111
Issue:
6
ISSN:
2470-0010
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
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