Dynamical Origin of the Lorentzian Signature of Spacetime

J. Greensite

doi:10.1016/0370-2693(93)90744-3

paper

Dynamical Origin of the Lorentzian Signature of Spacetime

arXiv:gr-qc/9210008 · doi:10.1016/0370-2693(93)90744-3

Abstract

It is suggested that not only the curvature, but also the signature of spacetime is subject to quantum fluctuations. A generalized D-dimensional spacetime metric of the form $g_{μν} = e_{μ}^{a} η_{ab} e_{ν}^{b}$ is introduced, where $η_{ab} = d ia g {e^{i θ}, 1, ..., 1}$ . The corresponding functional integral for quantized fields then interpolates from a Euclidean path integral in Euclidean space, at $θ = 0$ , to a Feynman path integral in Minkowski space, at $θ = π$ . Treating the phase $e^{i θ}$ as just another quantized field, the signature of spacetime is determined dynamically by its expectation value. The complex-valued effective potential $V (θ)$ for the phase field, induced by massless fields at one-loop, is considered. It is argued that $R e [V (θ)]$ is minimized and $I m [V (θ)]$ is stationary, uniquely in D=4 dimensions, at $θ = π$ , which suggests a dynamical origin for the Lorentzian signature of spacetime.

6 pages, LaTeX

Dynamical Origin of the Lorentzian Signature of Spacetime

Abstract

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