https://doi.org/10.1140/epjc/s10052-017-4855-0
Regular Article - Theoretical Physics
Hamiltonian approach to GR – Part 2: covariant theory of quantum gravity
1
Institute of Physics and Research Center for Theoretical Physics and Astrophysics, Faculty of Philosophy and Science, Silesian University in Opava, Bezručovo nám.13, 74601, Opava, Czech Republic
2
Department of Mathematics and Geosciences, University of Trieste, Via Valerio 12, 34127, Trieste, Italy
3
Institute of Physics, Faculty of Philosophy and Science, Silesian University in Opava, Bezručovo nám.13, 74601, Opava, Czech Republic
* e-mail: claudiocremaschini@gmail.com
Received:
6
January
2017
Accepted:
21
April
2017
Published online:
19
May
2017
A non-perturbative quantum field theory of General Relativity is presented which leads to a new realization of the theory of covariant quantum gravity (CQG-theory). The treatment is founded on the recently identified Hamiltonian structure associated with the classical space-time, i.e., the corresponding manifestly covariant Hamilton equations and the related Hamilton–Jacobi theory. The quantum Hamiltonian operator and the CQG-wave equation for the corresponding CQG-state and wave function are realized in 4-scalar form. The new quantum wave equation is shown to be equivalent to a set of quantum hydrodynamic equations which warrant the consistency with the classical GR Hamilton–Jacobi equation in the semiclassical limit. A perturbative approximation scheme is developed, which permits the adoption of the harmonic oscillator approximation for the treatment of the Hamiltonian potential. As an application of the theory, the stationary vacuum CQG-wave equation is studied, yielding a stationary equation for the CQG-state in terms of the 4-scalar invariant-energy eigenvalue associated with the corresponding approximate quantum Hamiltonian operator. The conditions for the existence of a discrete invariant-energy spectrum are pointed out. This yields a possible estimate for the graviton mass together with a new interpretation about the quantum origin of the cosmological constant.
© The Author(s), 2017
