Complex lapse, complex action and path integrals

Abstract

Imaginary time is often used in quantum tunnelling 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 which 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-tunnelling scenario for the origin of the universe. Taken as an explanation for the observed quantum tunnelling of particles, the complex-lapse theory determines that the argument of the lapse for the universe now is extremely small but negative.

12 pages, TeX

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Cited by in corpus (7)

• Emergent Models for Gravity: an Overview of Microscopic Models
• How to Wick rotate generic curved spacetime
• A Low Matter Density Decaying Vacuum Cosmology from Complex Metric
• Feynman's i-epsilon prescription, almost real spacetimes, and acceptable complex spacetimes
• A trick for passing degenerate points in Ashtekar formulation
• Singularity at the demise of a black hole
• Comment on "Comparison of approaches to classical signature change"