Friday, December 14, 2012

0902.2829 (L. A. Glinka)

On the residual effective potential within global one-dimensional
quantum gravity

L. A. Glinka
Gobal one-dimensional quantum gravity is the model of quantum gravity arising from global one-dimensionality conjecture within quantum general relativity, where the global dimension is determinant of metric of three-dimensional space embedded into enveloping Lorentizan spacetime of dimension four. The quantum--mechanical part of this model is a minimal effective model within the standard Wheeler--DeWitt quantum geometrodynamics, but the effective potential is manifestly different from the standard one and the wave functionals are globally one--dimensional. In this paper few selected elements of the globally one-dimensional quantum mechanics are discussed in some detail. The generalized functional expansion of the effective potential and the residual approximation of the expansion, which corresponds to the embeddings being the maximally symmetric three-dimensional Einstein manifolds whose the physical meaning is reconstruction the Newton-Coulomb type potential within the model of quantum gravity, are considered. Few possible mathematical scenarios with respect to the form of the effective potential are suggested as possibly interesting from the theoretical physics point of view.
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