Global one-dimensionality conjecture within quantum general relativity

Glinka, Łukasz Andrzej

doi:10.1134/s0202289310010020

Cited by 7 publications

(14 citation statements)

References 9 publications

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“…The global one-dimensionality conjecture within quantum general relativity [1,2] assumes the effective physical role of the determinant of a three-dimensional space embedded into a four-dimensional spacetime…”

Section: The Global Dimensionmentioning

confidence: 99%

“…It was recently proposed by the author, [1,2], to take into account the global one-dimensionality conjecture within quantum general relativity, where the global dimension is determinant of metric of a three-dimensional space embedded into four-dimensional space-time. Actually, this conjecture leads to the non-trivial model of quantum gravity which differs from the standardly considered approaches [3][4][5][6][7][8][9][10][11][12].…”

Section: Introductionmentioning

confidence: 99%

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On The Residual Effective Potential within Global One-Dimensional Quantum Gravity

Glinka¹

2014

J Astrophys Aerospace Technol

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The global one-dimensional quantum gravity is the model of quantum gravity which arises from the global onedimensionality 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.

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Section: The Global Dimensionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

On The Residual Effective Potential within Global One-Dimensional Quantum Gravity

Glinka¹

2014

J Astrophys Aerospace Technol

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“…Recently the Wheeler-DeWitt equation was considered in the framework of the global onedimensionality conjecture (Glinka, 2012;2010). Recall that this conjecture formally reduces the functional differential nature of the WheelerDeWitt quantum geometrodynamics throughout the primary canonical quantization of General Relativity in the Dirac-ArnowittDeser-Misner Hamiltonian formulation (Glinka, 2012;2010).…”

mentioning

confidence: 99%

“…Recall that this conjecture formally reduces the functional differential nature of the WheelerDeWitt quantum geometrodynamics throughout the primary canonical quantization of General Relativity in the Dirac-ArnowittDeser-Misner Hamiltonian formulation (Glinka, 2012;2010).…”

mentioning

confidence: 99%

“…This "global graviton" arises from a certain specific global optimization of the Wheeler-DeWitt quantum geometrodynamics and, for this reason, its physical existence is much more fundamental than the quanta of gravitation defined by the standard quantum geometrodynamics based on the Wheeler-DeWitt equation, as well as more likely than the gravitons understood in terms of the Yang-Mills theories, which constitute the leading reasoning line of modern particle physics (Cf. relevant references discussed in Glinka 2012;2010).…”

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confidence: 99%

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Do Global Virtual Axionic Gravitons Exist?

Glinka¹

2014

Neuroquantology

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Recently, the author has proposed the global one-dimensionality conjecture which, throughout making use of the method of the primary canonical quantization of General Relativity according to the Dirac-Arnowitt-Deser-Misner Hamiltonian formulation, formally avoids the functional differential nature which is the basic obstacle of quantum geometrodynamics, a model of quantum gravity based on the Wheeler-DeWitt equation and resutling from quantization of the Einstein field equations. The emergent quantum gravity model is straightforwardly integrable in terms of the Riemann-Lebesgue integral, has an unambiguous physical interpretation within quantum theory, and introduces a consistent concept of global graviton. In this article, the axionic nature of the global gravitons, that is the hypothetical particles responsible for gravitation in the global one-dimensional quantum gravity model, is shortly described and, making use of fundamental methods of quantum field theory, the virtual states of such gravitons are generated.

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Novel Solution of Wheeler-DeWitt Theory

Glinka¹

2014

AMP

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Taking into account the global one-dimensionality conjecture recently proposed by the author, the Cauchy-like analytical wave functional of the Wheeler-DeWitt theory is derived. The crucial point of the integration strategy is canceling of the singular behavior of the effective potential, which is performed through the suitable change of variables introducing the invariant global dimension. In addition, the conjecture is extended onto the wave functionals dependent on both Matter felids as well as the invariant global dimension. Through application of the reduction within the quantum gravity model, the appropriate Dirac equation is obtained and than solved. The case of superposition is also briey discussed.

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Global one-dimensionality conjecture within quantum general relativity

Cited by 7 publications

References 9 publications

On The Residual Effective Potential within Global One-Dimensional Quantum Gravity

On The Residual Effective Potential within Global One-Dimensional Quantum Gravity

Do Global Virtual Axionic Gravitons Exist?

Novel Solution of Wheeler-DeWitt Theory

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