Coupling of quantum gravitational field with Riemann and Ricci curvature tensors

@article{57642,
   author = {Cremaschini, Claudio and Tessarotto, Massimo},
   article_location = {New York (USA)},
   article_number = {6},
   doi = {http://dx.doi.org/10.1140/epjc/s10052-021-09343-x},
   keywords = {quantum gravitational field with;Ricci and Riemann curvature tensors;General Relativity},
   language = {eng},
   issn = {1434-6044},
   journal = {European Physical Journal C},
   title = {Coupling of quantum gravitational field with Riemann and Ricci curvature tensors},
   url = {https://link.springer.com/article/10.1140/epjc/s10052-021-09343-x},
   volume = {81},
   year = {2021}
}

TY  - JOUR
ID  - 57642
AU  - Cremaschini, Claudio - Tessarotto, Massimo
PY  - 2021
TI  - Coupling of quantum gravitational field with Riemann and Ricci curvature tensors
JF  - European Physical Journal C
VL  - 81
IS  - 6
SP  - "548-1"-"548-13"
EP  - "548-1"-"548-13"
PB  - SPRINGER
SN  - 14346044
KW  - quantum gravitational field with;Ricci and Riemann curvature tensors;General Relativity
UR  - https://link.springer.com/article/10.1140/epjc/s10052-021-09343-x
N2  - The theoretical problem of establishing the coupling properties existing between the classical and quantum gravitational field with the Ricci and Riemann curvature tensors of General Relativity is addressed. The mathematical framework is provided by synchronous Hamilton variational principles and the validity of classical and quantum canonical Hamiltonian structures for the gravitational field dynamics. It is shown that, for the classical variational theory, manifestly-covariant Hamiltonian functions expressed by either the Ricci or Riemann tensors are both admitted, which yield the correct form of Einstein field equations. On the other hand, the corresponding realization of manifestly-covariant quantum gravity theories is not equivalent. The requirement imposed is that the Hamiltonian potential should represent a positive-definite quadratic form when performing a quadratic expansion around the equilibrium solution. This condition in fact warrants the existence of positive eigenvalues of the quantum Hamiltonian in the harmonic-oscillator representation, to be related to the graviton mass. Accordingly, it is shown that in the background of the deSitter space-time, only the Ricci tensor coupling is physically admitted. In contrast, the coupling of quantum gravitational field with the Riemann tensor generally prevents the possibility of achieving a Hamiltonian potential appropriate for the implementation of the quantum harmonic-oscillator solution.
ER  - 

CREMASCHINI, Claudio a Massimo TESSAROTTO. Coupling of quantum gravitational field with Riemann and Ricci curvature tensors. \textit{European Physical Journal C}. New York (USA): SPRINGER, 2021, roč.~81, č.~6, s.~''548-1''-''548-13'', 13 s. ISSN~1434-6044. Dostupné z: https://dx.doi.org/10.1140/epjc/s10052-021-09343-x.