The Dynamical Evolution Parameter in Manifestly Covariant Quantum Gravity Theory

A remarkable feature of manifestly covariant quantum gravity theory (CQG-theory) is represented by its unconstrained Hamiltonian structure expressed in evolution form. This permits the identification of the corresponding dynamical evolution parameter advancing the quantum-wave equation for the <i...

Full description

Saved in:
Bibliographic Details
Main Author: Claudio Cremaschini
Format: Article
Language:English
Published: MDPI AG 2025-06-01
Series:Entropy
Subjects:
Online Access:https://www.mdpi.com/1099-4300/27/6/604
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:A remarkable feature of manifestly covariant quantum gravity theory (CQG-theory) is represented by its unconstrained Hamiltonian structure expressed in evolution form. This permits the identification of the corresponding dynamical evolution parameter advancing the quantum-wave equation for the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>4</mn><mo>−</mo></mrow></semantics></math></inline-formula>scalar quantum wave function defined on an appropriate Hilbert space. In the framework of CQG-theory, such a temporal parameter is represented by a <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>4</mn><mo>−</mo></mrow></semantics></math></inline-formula>scalar proper time <i>s</i> identifying a canonical variable with conjugate quantum operator. The observable character of the evolution parameter is also established through its correspondence with the quantum representation of the cosmological constant originating from non-linear Bohm quantum–vacuum interaction, which is shown to admit an intrinsic functional dependence on <i>s</i>. These conclusions overcome the conceptual limitations about the so-called “problem of time” mentioned in alternative approaches to quantum gravity available in the literature. Hence, the outcome permits one to promote CQG theory as a viable mathematical setting for the establishment of a theory of quantum gravity consistent with the logical and physical principles of both general relativity and canonical quantum mechanics.
ISSN:1099-4300