On The Residual Effective Potential within Global One-Dimensional Quantum Gravity
Lukasz Andrzej Glinka*
Member of the American Association of International Researchers. New York, USA
- *Corresponding Author:
- Lukasz Andrzej Glinka
Member of the American Association of International Researchers
New York, USA
E-mail: [email protected]
Received Date: February 05, 2014; Accepted Date: February 25, 2014; Published Date: March 05, 2014
Citation: Glinka LA (2014) On The Residual Effective Potential within Global One-Dimensional Quantum Gravity. J Astrophys Aerospace Technol 2:103. doi: 10.4172/2329-6542.1000.103
Copyright: © 2014 Glinka LA. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.
The global one-dimensional quantum gravity is the model of quantum gravity which arises from the global one dimensionality conjecture within quantum general relativity, first considered by the author in 2010 and then in 2012. In this model the global dimension is a determinant of a metric of three-dimensional space embedded into an enveloping Lorentizan four-dimensional space-time. In 2012, it has already been presented by the author that this model can be extended to any Lorentzian D + 1-dimensional space-time, where D is a dimension of space, and resulting in the global one-dimensional model of a higher dimensional quantum gravity. The purely quantum–mechanical part of this model is a minimal effective model within the quantum Geometrodynamics, introduced by J.A. Wheeler and B.S. DeWitt in the 1960s, but the effective potential is manifestly different from the one considered by Wheeler & DeWitt. Moreover, in our model the wave functionals solving the quantum gravity are one-variable smooth functions and, therefore, the troublesome mathematical technique of the Feynman functional integration present in the Hawking formulation of quantum gravity, is absent is this model, what makes it a mathematically consistent theory of quantum gravitation. In this paper, we discuss in some detail a certain part of the global one-dimensional model already proposed in 2010, and then developed in 2012. The generalized functional expansion of the effective potential and the residual approximation, which describe the embedded spaces which are maximally symmetric three-dimensional Einstein’s manifolds, whose lead to the Newton–Coulomb type potential in the quantum gravity model, are considered. Furthermore, scenarios related to few selected specific forms of the effective potential are suggested as physically interesting and discussed.