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Dynamical Origin of the Lorentzian Signature of Spacetime | | J. Greensite
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14 Oct 1992 | | Journal: | Phys. Lett. B300 (1993) 34-37 | | Subject: | gr-qc hep-th | | 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 $g_{mu
u}=e^a_mu eta_{ab} e^b_
u$ is introduced, where $eta_{ab} = diag{e^{i heta},1,...,1}$. The corresponding functional integral for quantized fields then interpolates from a Euclidean path integral in Euclidean space, at $ heta=0$, to a Feynman path integral in Minkowski space, at $ heta=pi$. Treating the phase $e^{i heta}$ as just another quantized field, the signature of spacetime is determined dynamically by its expectation value. The complex-valued effective potential $V( heta)$ for the phase field, induced by massless fields at one-loop, is considered. It is argued that $Re[V( heta)]$ is minimized and $Im[V( heta)]$ is stationary, uniquely in D=4 dimensions, at $ heta=pi$, which suggests a dynamical origin for the Lorentzian signature of spacetime. | | Source: | arXiv, gr-qc/9210008 | | Services: | Forum | Review | PDF | Favorites | |
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