Generalized Lagrangian Path Approach to Manifestly-Covariant Quantum Gravity Theory
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-rep...
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MDPI AG
2018-03-01
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| Series: | Entropy |
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| Online Access: | http://www.mdpi.com/1099-4300/20/3/205 |
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| author | Massimo Tessarotto Claudio Cremaschini |
| author_facet | Massimo Tessarotto Claudio Cremaschini |
| author_sort | Massimo Tessarotto |
| collection | DOAJ |
| description | 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. |
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| id | doaj.art-3271cf5a2d64482586a1cd64a7dcd8e0 |
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| issn | 1099-4300 |
| language | English |
| last_indexed | 2024-04-14T02:24:19Z |
| publishDate | 2018-03-01 |
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| spelling | doaj.art-3271cf5a2d64482586a1cd64a7dcd8e02022-12-22T02:17:56ZengMDPI AGEntropy1099-43002018-03-0120320510.3390/e20030205e20030205Generalized Lagrangian Path Approach to Manifestly-Covariant Quantum Gravity TheoryMassimo Tessarotto0Claudio Cremaschini1Department of Mathematics and Geosciences, University of Trieste, Via Valerio 12, 34127 Trieste, ItalyInstitute 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 RepublicA 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.http://www.mdpi.com/1099-4300/20/3/205quantum mechanicsgeneralized Lagrangian pathscovariant quantum gravityemergent space-timeGaussian-like solutions |
| spellingShingle | Massimo Tessarotto Claudio Cremaschini Generalized Lagrangian Path Approach to Manifestly-Covariant Quantum Gravity Theory Entropy quantum mechanics generalized Lagrangian paths covariant quantum gravity emergent space-time Gaussian-like solutions |
| title | Generalized Lagrangian Path Approach to Manifestly-Covariant Quantum Gravity Theory |
| title_full | Generalized Lagrangian Path Approach to Manifestly-Covariant Quantum Gravity Theory |
| title_fullStr | Generalized Lagrangian Path Approach to Manifestly-Covariant Quantum Gravity Theory |
| title_full_unstemmed | Generalized Lagrangian Path Approach to Manifestly-Covariant Quantum Gravity Theory |
| title_short | Generalized Lagrangian Path Approach to Manifestly-Covariant Quantum Gravity Theory |
| title_sort | generalized lagrangian path approach to manifestly covariant quantum gravity theory |
| topic | quantum mechanics generalized Lagrangian paths covariant quantum gravity emergent space-time Gaussian-like solutions |
| url | http://www.mdpi.com/1099-4300/20/3/205 |
| work_keys_str_mv | AT massimotessarotto generalizedlagrangianpathapproachtomanifestlycovariantquantumgravitytheory AT claudiocremaschini generalizedlagrangianpathapproachtomanifestlycovariantquantumgravitytheory |