On the residual effective potential within Global 1D Quantum Gravity

Details On the residual effective potential within Global 1D Quantum Gravity On the residual effective potential within Global 1D Quantum Gravity

2009-02-17

arxiv.org/abs/0902.2829v1

Physics

High Energy Physics

High Energy Physics - Theory

27 pages, no figures

Scientific paper

The conjecture on Global One-Dimensionality within Quantum General Relativity leads to the model of quantum gravity possessing nontrivial field theoretic content. This is a midisuperspatial model, which quantum mechanical part can be considered independently. The fragment, basing on the Dirac-Faddeev canonical primary quantization of Hamiltonian constraint, in fact constitutes minimal effective model within standard quantum geometrodynamics with potential different from the standard. It uses one-dimensional wave functions, where the (global) dimension is a volume form of a 3-embedding. In this paper some elements of the global 1D quantum mechanics are presented. We consider absence of matter fields. Generalized functional expansion in the global dimension of the effective potential is discussed. Finally, its residual approximation, the Newton-Coulomb type potential, realized by all embeddings being maximally symmetric 3-dimensional Einstein manifolds is studied.

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