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Article

Generalized Lagrangian Path Approach to Manifestly-Covariant Quantum Gravity Theory

1
Department of Mathematics and Geosciences, University of Trieste, Via Valerio 12, 34127 Trieste, Italy
2
Institute of Physics, Faculty of Philosophy and Science, Silesian University in Opava, Bezručovo nám.13, CZ-74601 Opava, Czech Republic
3
Institute of Physics and Research Center for Theoretical Physics and Astrophysics, Faculty of Philosophy and Science, Silesian University in Opava, Bezručovo nám.13, CZ-74601 Opava, Czech Republic
*
Author to whom correspondence should be addressed.
Entropy 2018, 20(3), 205; https://doi.org/10.3390/e20030205
Received: 10 January 2018 / Revised: 25 February 2018 / Accepted: 8 March 2018 / Published: 19 March 2018
(This article belongs to the Special Issue Emergent Quantum Mechanics – David Bohm Centennial Perspectives)
A trajectory-based representation for the quantum theory of the gravitational field is formulated. This is achieved in terms of a covariant Generalized Lagrangian-Path (GLP) approach which relies on a suitable statistical representation of Bohmian Lagrangian trajectories, referred to here as GLP-representation. The result is established in the framework of the manifestly-covariant quantum gravity theory (CQG-theory) proposed recently and the related CQG-wave equation advancing in proper-time the quantum state associated with massive gravitons. Generally non-stationary analytical solutions for the CQG-wave equation with non-vanishing cosmological constant are determined in such a framework, which exhibit Gaussian-like probability densities that are non-dispersive in proper-time. As a remarkable outcome of the theory achieved by implementing these analytical solutions, the existence of an emergent gravity phenomenon is proven to hold. Accordingly, it is shown that a mean-field background space-time metric tensor can be expressed in terms of a suitable statistical average of stochastic fluctuations of the quantum gravitational field whose quantum-wave dynamics is described by GLP trajectories. View Full-Text
Keywords: quantum mechanics; generalized Lagrangian paths; covariant quantum gravity; emergent space-time; Gaussian-like solutions quantum mechanics; generalized Lagrangian paths; covariant quantum gravity; emergent space-time; Gaussian-like solutions
MDPI and ACS Style

Tessarotto, M.; Cremaschini, C. Generalized Lagrangian Path Approach to Manifestly-Covariant Quantum Gravity Theory. Entropy 2018, 20, 205. https://doi.org/10.3390/e20030205

AMA Style

Tessarotto M, Cremaschini C. Generalized Lagrangian Path Approach to Manifestly-Covariant Quantum Gravity Theory. Entropy. 2018; 20(3):205. https://doi.org/10.3390/e20030205

Chicago/Turabian Style

Tessarotto, Massimo, and Claudio Cremaschini. 2018. "Generalized Lagrangian Path Approach to Manifestly-Covariant Quantum Gravity Theory" Entropy 20, no. 3: 205. https://doi.org/10.3390/e20030205

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