Complex lapse, complex action, and path integrals

Sean A. Hayward
Phys. Rev. D 53, 5664 – Published 15 May 1996
PDFExport Citation

Abstract

Imaginary time is often used in quantum tunneling calculations. This article advocates a conceptually sounder alternative: complex lapse. In the "3+1" action for the Einstein gravitational field minimally coupled to a Klein-Gordon field, allowing the lapse function to be complex yields a complex action that generates both the usual Lorentzian theory and its Riemannian analogue and in particular allows a change of signature between the two. The action and variational equations are manifestly well defined in the Hamiltonian representation, with the momentum fields consequently being complex. The complex action interpolates between the Lorentzian and Riemannian actions as they appear formally in the respective path integrals. Thus the complex-lapse theory provides a unified basis for a path-integral quantum theory of gravity involving both Lorentzian and Riemannian aspects. A major motivation is the quantum-tunneling scenario for the origin of the universe. Taken as an explanation for the observed quantum tunneling of particles, the complex-lapse theory determines that the argument of the lapse for the universe now is extremely small but negative.

  • Received 2 November 1995

DOI:https://doi.org/10.1103/PhysRevD.53.5664

©1996 American Physical Society

Authors & Affiliations

Sean A. Hayward*

  • Department of Physics, Kyoto University, Kyoto 606-01, Japan

  • *Electronic address: hayward@murasaki.scphys.kyoto-u.ac.jp

References (Subscription Required)

Click to Expand
Issue

Vol. 53, Iss. 10 — 15 May 1996

Reuse & Permissions
Access Options
Author publication services for translation and copyediting assistance advertisement

Authorization Required


×
×

Images

×

Sign up to receive regular email alerts from Physical Review D

Log In

Cancel
×

Search


Article Lookup

Paste a citation or DOI

Enter a citation
×