Next Article in Journal
Irreversibility and Action of the Heat Conduction Process
Next Article in Special Issue
The Definition of Entropy for Quantum Unstable Systems: A View-Point Based on the Properties of Gamow States
Previous Article in Journal
Output-Feedback Control for Discrete-Time Spreading Models in Complex Networks
Previous Article in Special Issue
Why Bohmian Mechanics? One- and Two-Time Position Measurements, Bell Inequalities, Philosophy, and Physics
Article Menu
Issue 3 (March) cover image

Export Article

Open AccessArticle
Entropy 2018, 20(3), 205; https://doi.org/10.3390/e20030205

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.
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)
Full-Text   |   PDF [410 KB, uploaded 19 March 2018]

Abstract

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
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).
SciFeed

Share & Cite This Article

MDPI and ACS Style

Tessarotto, M.; Cremaschini, C. Generalized Lagrangian Path Approach to Manifestly-Covariant Quantum Gravity Theory. Entropy 2018, 20, 205.

Show more citation formats Show less citations formats

Note that from the first issue of 2016, MDPI journals use article numbers instead of page numbers. See further details here.

Related Articles

Article Metrics

Article Access Statistics

1

Comments

[Return to top]
Entropy EISSN 1099-4300 Published by MDPI AG, Basel, Switzerland RSS E-Mail Table of Contents Alert
Back to Top