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...
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2025-06-01
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| author | Claudio Cremaschini |
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| description | 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. |
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| spelling | doaj-art-22f33751b4a149a88f1015745b72b14e2025-08-20T03:24:35ZengMDPI AGEntropy1099-43002025-06-0127660410.3390/e27060604The Dynamical Evolution Parameter in Manifestly Covariant Quantum Gravity TheoryClaudio Cremaschini0Research Centre for Theoretical Physics and Astrophysics, Institute of Physics, Silesian University in Opava, Bezručovo nám.13, CZ-74601 Opava, Czech RepublicA 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.https://www.mdpi.com/1099-4300/27/6/604covariant quantum gravityHamiltonian theoryevolution parametercosmological constant |
| spellingShingle | Claudio Cremaschini The Dynamical Evolution Parameter in Manifestly Covariant Quantum Gravity Theory Entropy covariant quantum gravity Hamiltonian theory evolution parameter cosmological constant |
| title | The Dynamical Evolution Parameter in Manifestly Covariant Quantum Gravity Theory |
| title_full | The Dynamical Evolution Parameter in Manifestly Covariant Quantum Gravity Theory |
| title_fullStr | The Dynamical Evolution Parameter in Manifestly Covariant Quantum Gravity Theory |
| title_full_unstemmed | The Dynamical Evolution Parameter in Manifestly Covariant Quantum Gravity Theory |
| title_short | The Dynamical Evolution Parameter in Manifestly Covariant Quantum Gravity Theory |
| title_sort | dynamical evolution parameter in manifestly covariant quantum gravity theory |
| topic | covariant quantum gravity Hamiltonian theory evolution parameter cosmological constant |
| url | https://www.mdpi.com/1099-4300/27/6/604 |
| work_keys_str_mv | AT claudiocremaschini thedynamicalevolutionparameterinmanifestlycovariantquantumgravitytheory AT claudiocremaschini dynamicalevolutionparameterinmanifestlycovariantquantumgravitytheory |