TESSAROTTO, Massimo and Claudio CREMASCHINI. Background Independence and Gauge Invariance in General Relativity Part 2-Covariant Quantum Gravity. SYMMETRY-BASEL. Švýcarsko, 2022, vol. 14, No 11, p. "2229-1"-"2229-23", 23 pp. ISSN 2073-8994. Available from: https://dx.doi.org/10.3390/sym14112229.
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Basic information
Original name Background Independence and Gauge Invariance in General Relativity Part 2-Covariant Quantum Gravity
Authors TESSAROTTO, Massimo (380 Italy, belonging to the institution) and Claudio CREMASCHINI (380 Italy, belonging to the institution).
Edition SYMMETRY-BASEL, Švýcarsko, 2022, 2073-8994.
Other information
Original language English
Type of outcome Article in a journal
Field of Study 10308 Astronomy
Country of publisher Switzerland
Confidentiality degree is not subject to a state or trade secret
WWW URL
RIV identification code RIV/47813059:19630/22:A0000214
Organization unit Institute of physics in Opava
Doi http://dx.doi.org/10.3390/sym14112229
UT WoS 000881496800001
Keywords in English Hamiltonian theory of GR; manifest covariance; covariant quantum gravity; background independence; emergent gravity
Tags FÚ, RIV23
Tags International impact, Reviewed
Changed by Changed by: Mgr. Pavlína Jalůvková, učo 25213. Changed: 31/1/2023 12:11.
Abstract
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.
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