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arXiv · 1412.4740

Wheeler-DeWitt Equation for 4D Supermetric and ADM with Massless Scalar Field as Internal Time

Leonid Perlov
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Abstract

The main result of this paper is the 4-dimensional supermetric version of the Wheeler-DeWitt equation, that uses only one time variable for the both roles - as internal time and for the ADM split, as Hamiltonian evolution parameter. We study the ADM split with respect to the scalar massless field serving as internal time. The 4-dimensional hyper-surfaces $Σ_{ϕ= const}$ span the 5-dimensional space with the scalar field being the fifth coordinate. As a result we obtain the analog of the Wheeler-DeWitt equation for the 4-dimensional supermetric. We compare the ADM action with the non-compactified Kaluza-Klein action for the same physical space and obtain the equation for the extrinsic curvature and the scalar massless field.

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Leonid Perlov. 2015-02-14. Wheeler-DeWitt Equation for 4D Supermetric and ADM with Massless Scalar Field as Internal Time. https://doi.org/10.1016/j.physletb.2015.02.030

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