Generalized Lagrangian Path Approach to Manifestly-Covariant Quantum Gravity Theory

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.

Space-Time Second-Quantization Effects and the Quantum Origin of Cosmological Constant in Covariant Quantum Gravity

“…The theory of manifestly-covariant quantum gravity (CQG-theory) recently proposed in a series of papers (see Refs. [1][2][3][4][5][6]) provides a possible new self-consistent route to Quantum Gravity and the cosmological interpretation of quantum vacuum. This refers specifically to the quantum prescription of the cosmological constant and the longstanding question whether or not it can be ascribed exclusively to suitable vacuum fluctuations arising at the quantum level.…”

“…CQG-theory realizes, as such, a first-quantization picture of space-time which embodies simultaneously all the required fundamental principles (for an extended related discussion we refer again to Refs. [1][2][3][4][5][6]). One of its notable features is realized, first of all, by the distinction between a continuum classical background metric tensor g ≡ { g µν }, yielding the geometric properties of the space-time, and the quantum gravitational field g µν which dynamically evolves over g according to a defined quantum wave equation (CQG-wave equation) [4].…”

“…• The formulation of a trajectory-based representation of CQG-theory achieved in terms of a covariant Generalized Lagrangian-Path (GLP) approach relying on a suitable statistical representation of Bohmian Lagrangian trajectories [6,15].…”

“…• The construction of generally non-stationary analytical solutions for the CQG-wave equation with non-vanishing cosmological constant and exhibiting Gaussian-like probability densities that are non-dispersive in proper-time [6].…”

“…• The proof of the existence of an emergent gravity phenomenon occurring in the context of CQG-theory (previously referred to as "second-type emergent-gravity paradigm" (see Ref. [6])) according to which it can/must be possible to represent the mean-field background space-time metric tensor g in terms of a suitable ensemble average. More precisely, as shown in the same reference, this is identified in terms of a statistical average with respect to stochastic fluctuations of the quantum gravitational field g µν , whose quantum-wave dynamics is actually described by means of GLP trajectories [6].…”