Quantum-Wave Equation and Heisenberg Inequalities of Covariant Quantum Gravity

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F47813059%3A19240%2F17%3AA0000014" target="_blank" >RIV/47813059:19240/17:A0000014 - isvavai.cz</a>

Výsledek na webu

<a href="http://www.mdpi.com/1099-4300/19/7/339" target="_blank" >http://www.mdpi.com/1099-4300/19/7/339</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.3390/e19070339" target="_blank" >10.3390/e19070339</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Quantum-Wave Equation and Heisenberg Inequalities of Covariant Quantum Gravity

Popis výsledku v původním jazyce

Key aspects of the manifestly-covariant theory of quantum gravity (Cremaschini and Tessarotto 2015-2017) are investigated. These refer, first, to the establishment of the four-scalar, manifestly-covariant evolution quantum wave equation, denoted as covariant quantum gravity (CQG) wave equation, which advances the quantum state psi associated with a prescribed background space-time. In this paper, the CQG-wave equation is proved to follow at once by means of a Hamilton-Jacobi quantization of the classical variational tensor field g equivalent to {g_(mu nu)} and its conjugate momentum, referred to as (canonical) g-quantization. The same equation is also shown to be variational and to follow from a synchronous variational principle identified here with the quantum Hamilton variational principle. The corresponding quantum hydrodynamic equations are then obtained upon introducing the Madelung representation for psi, which provides an equivalent statistical interpretation of the CQG-wave equation. Finally, the quantum state y is proven to fulfill generalized Heisenberg inequalities, relating the statistical measurement errors of quantum observables. These are shown to be represented in terms of the standard deviations of the metric tensor g equivalent to {g_(mu nu)} and its quantum conjugate momentum operator.

Název v anglickém jazyce

Quantum-Wave Equation and Heisenberg Inequalities of Covariant Quantum Gravity

Popis výsledku anglicky

Key aspects of the manifestly-covariant theory of quantum gravity (Cremaschini and Tessarotto 2015-2017) are investigated. These refer, first, to the establishment of the four-scalar, manifestly-covariant evolution quantum wave equation, denoted as covariant quantum gravity (CQG) wave equation, which advances the quantum state psi associated with a prescribed background space-time. In this paper, the CQG-wave equation is proved to follow at once by means of a Hamilton-Jacobi quantization of the classical variational tensor field g equivalent to {g_(mu nu)} and its conjugate momentum, referred to as (canonical) g-quantization. The same equation is also shown to be variational and to follow from a synchronous variational principle identified here with the quantum Hamilton variational principle. The corresponding quantum hydrodynamic equations are then obtained upon introducing the Madelung representation for psi, which provides an equivalent statistical interpretation of the CQG-wave equation. Finally, the quantum state y is proven to fulfill generalized Heisenberg inequalities, relating the statistical measurement errors of quantum observables. These are shown to be represented in terms of the standard deviations of the metric tensor g equivalent to {g_(mu nu)} and its quantum conjugate momentum operator.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10308 - Astronomy (including astrophysics,space science)

Projekt

Výsledek vznikl pri realizaci vícero projektů. Více informací v záložce Projekty.

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)<br>I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2017

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

Entropy

ISSN

1099-4300

e-ISSN

—

Svazek periodika

19

Číslo periodika v rámci svazku

7

Stát vydavatele periodika

CH - Švýcarská konfederace

Počet stran výsledku

20

Strana od-do

'339-1'-'339-20'

Kód UT WoS článku

000406701500049

EID výsledku v databázi Scopus

2-s2.0-85022203801