J 2021

Coupling of quantum gravitational field with Riemann and Ricci curvature tensors

CREMASCHINI, Claudio a Massimo TESSAROTTO

Základní údaje

Originální název

Coupling of quantum gravitational field with Riemann and Ricci curvature tensors

Autoři

CREMASCHINI, Claudio (380 Itálie, domácí) a Massimo TESSAROTTO (380 Itálie, domácí)

Vydání

European Physical Journal C, New York (USA), SPRINGER, 2021, 1434-6044

Další údaje

Jazyk

angličtina

Typ výsledku

Článek v odborném periodiku

Obor

10308 Astronomy

Stát vydavatele

Spojené státy

Utajení

není předmětem státního či obchodního tajemství

Odkazy

Kód RIV

RIV/47813059:19630/21:A0000146

Organizační jednotka

Fyzikální ústav v Opavě

UT WoS

000680462500005

Klíčová slova anglicky

quantum gravitational field with;Ricci and Riemann curvature tensors;General Relativity

Štítky

Příznaky

Mezinárodní význam, Recenzováno
Změněno: 8. 2. 2022 15:32, Mgr. Pavlína Jalůvková

Anotace

V originále

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.