CREMASCHINI, Claudio and Massimo TESSAROTTO. Coupling of quantum gravitational field with Riemann and Ricci curvature tensors. European Physical Journal C. New York (USA): SPRINGER, 2021, vol. 81, No 6, p. "548-1"-"548-13", 13 pp. ISSN 1434-6044. Available from: https://dx.doi.org/10.1140/epjc/s10052-021-09343-x.
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Basic information
Original name Coupling of quantum gravitational field with Riemann and Ricci curvature tensors
Authors CREMASCHINI, Claudio (380 Italy, belonging to the institution) and Massimo TESSAROTTO (380 Italy, belonging to the institution).
Edition European Physical Journal C, New York (USA), SPRINGER, 2021, 1434-6044.
Other information
Original language English
Type of outcome Article in a journal
Field of Study 10308 Astronomy
Country of publisher United States of America
Confidentiality degree is not subject to a state or trade secret
WWW URL
RIV identification code RIV/47813059:19630/21:A0000146
Organization unit Institute of physics in Opava
Doi http://dx.doi.org/10.1140/epjc/s10052-021-09343-x
UT WoS 000680462500005
Keywords in English quantum gravitational field with;Ricci and Riemann curvature tensors;General Relativity
Tags 2022, FÚ, RIV22
Tags International impact, Reviewed
Changed by Changed by: Mgr. Pavlína Jalůvková, učo 25213. Changed: 8/2/2022 15:32.
Abstract
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.
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