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

@article{65828,
   author = {Tessarotto, Massimo and Cremaschini, Claudio},
   article_location = {Švýcarsko},
   article_number = {11},
   doi = {http://dx.doi.org/10.3390/sym14112229},
   keywords = {Hamiltonian theory of GR; manifest covariance; covariant quantum gravity; background independence; emergent gravity},
   language = {eng},
   issn = {2073-8994},
   journal = {SYMMETRY-BASEL},
   title = {Background Independence and Gauge Invariance in General Relativity Part 2-Covariant Quantum Gravity},
   url = {https://www.mdpi.com/2073-8994/14/11/2229},
   volume = {14},
   year = {2022}
}

TY  - JOUR
ID  - 65828
AU  - Tessarotto, Massimo - Cremaschini, Claudio
PY  - 2022
TI  - Background Independence and Gauge Invariance in General Relativity Part 2-Covariant Quantum Gravity
JF  - SYMMETRY-BASEL
VL  - 14
IS  - 11
SP  - "2229-1"-"2229-23"
EP  - "2229-1"-"2229-23"
SN  - 20738994
KW  - Hamiltonian theory of GR
KW  - manifest covariance
KW  - covariant quantum gravity
KW  - background independence
KW  - emergent gravity
UR  - https://www.mdpi.com/2073-8994/14/11/2229
N2  - 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.
ER  - 

TESSAROTTO, Massimo a Claudio CREMASCHINI. Background Independence and Gauge Invariance in General Relativity Part 2-Covariant Quantum Gravity. \textit{SYMMETRY-BASEL}. Švýcarsko, 2022, roč.~14, č.~11, s.~''2229-1''-''2229-23'', 23 s. ISSN~2073-8994. Dostupné z: https://dx.doi.org/10.3390/sym14112229.