Background Independence and Gauge Invariance in General Relativity Part 2-Covariant Quantum Gravity

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F47813059%3A19630%2F22%3AA0000214" target="_blank" >RIV/47813059:19630/22:A0000214 - isvavai.cz</a>

Výsledek na webu

<a href="https://www.mdpi.com/2073-8994/14/11/2229" target="_blank" >https://www.mdpi.com/2073-8994/14/11/2229</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.3390/sym14112229" target="_blank" >10.3390/sym14112229</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Background Independence and Gauge Invariance in General Relativity Part 2-Covariant Quantum Gravity

Popis výsledku v původním jazyce

Background independence is often being claimed as the characteristic property of several current and past models of Quantum Gravity. In actual fact, such a notion has a wider connotation and must be rooted into the validity of the general covariance principle, demanding its logical connection with the notions of manifest covariance and (quantum) gauge invariance. In fact, as we intend to show here, it involves (a) the existence of a well-defined, albeit arbitrary, classical background space-time; and (b) the suitable realization of a dynamical equation for the related background metric field tensor, referred to as quantum-modified Einstein tensor field equation, which actually determines it in a suitable functional setting. Remarkably, it is proved that in the context of the theory of Covariant Quantum Gravity (CQG-theory), recently developed by Cremaschini and Tessarotto (2015-2022), background independence implies that such an equation "emerges" rigorously from the same CQG-theory. This follows in terms of a stochastic quantum expectation value evaluated with respect to the corresponding characteristic quantum PDE. It is shown that an analogous emergence property applies also to the background metric field tensor in terms of stochastic fluctuations of the corresponding underlying quantum tensor of gravitational field. These results warrant the consistent validity of background independence for the prescription of the space-time metric tensor in CQG-theory.

Název v anglickém jazyce

Background Independence and Gauge Invariance in General Relativity Part 2-Covariant Quantum Gravity

Popis výsledku anglicky

Background independence is often being claimed as the characteristic property of several current and past models of Quantum Gravity. In actual fact, such a notion has a wider connotation and must be rooted into the validity of the general covariance principle, demanding its logical connection with the notions of manifest covariance and (quantum) gauge invariance. In fact, as we intend to show here, it involves (a) the existence of a well-defined, albeit arbitrary, classical background space-time; and (b) the suitable realization of a dynamical equation for the related background metric field tensor, referred to as quantum-modified Einstein tensor field equation, which actually determines it in a suitable functional setting. Remarkably, it is proved that in the context of the theory of Covariant Quantum Gravity (CQG-theory), recently developed by Cremaschini and Tessarotto (2015-2022), background independence implies that such an equation "emerges" rigorously from the same CQG-theory. This follows in terms of a stochastic quantum expectation value evaluated with respect to the corresponding characteristic quantum PDE. It is shown that an analogous emergence property applies also to the background metric field tensor in terms of stochastic fluctuations of the corresponding underlying quantum tensor of gravitational field. These results warrant the consistent validity of background independence for the prescription of the space-time metric tensor in CQG-theory.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10308 - Astronomy (including astrophysics,space science)

Projekt

—

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2022

Kód důvěrnosti údajů

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

Název periodika

SYMMETRY-BASEL

ISSN

2073-8994

e-ISSN

—

Svazek periodika

14

Číslo periodika v rámci svazku

11

Stát vydavatele periodika

CH - Švýcarská konfederace

Počet stran výsledku

23

Strana od-do

„2229-1“-„2229-23“

Kód UT WoS článku

000881496800001

EID výsledku v databázi Scopus

2-s2.0-85141695550