ADM with Massless Scalar Field as Internal Time and Wheeler-DeWitt Equation for 4D Supermetric
Year: 2014
Type: preprint
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 $\Sigma_{\phi = const}$ 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.
Source: arXiv (Cornell University)
Author: Leonid Perlov
Language: English
Subfield: Astronomy and Astrophysics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2275229632