Quantum Gravity in Heisenberg Representation and Self-Consistent Theory of Gravitons in Macroscopic Spacetime

Abstract

The first mathematically consistent exact equations of quantum gravity in the Heisenberg representation and Hamilton gauge are obtained. It is shown that the path integral over the canonical variables in the Hamilton gauge is mathematically equivalent to the operator equations of quantum theory of gravity with canonical rules of quantization of the gravitational and ghost fields. In its operator formulation, the theory can be used to calculate the graviton S-matrix as well as to describe the quantum evolution of macroscopic system of gravitons in the non-stationary Universe or in the vicinity of relativistic objects. In the S-matrix case, the standard results are obtained. For problems of the second type, the original Heisenberg equations of quantum gravity are converted to a self-consistent system of equations for the metric of the macroscopic space time and Heisenberg operators of quantum fields. It is shown that conditions of the compatibility and internal consistency of this system of equations are performed without restrictions on the amplitude and wavelength of gravitons and ghosts. The status of ghost fields in the various formulations of quantum theory of gravity is discussed.

Dark energy and inflation in a gravitational wave dominated universe

“…The exact equations of self-consistent theory of gravitons in the Heisenberg representation with the ghost sector automatically providing one-loop finiteness off the mass shell are obtained in our work [16]. In [16] were incorrect (see [16] and references therein).…”

“…This paper represents an attempt to gather together new and published results with emphasis on their cosmological applications (the effects of inflation and dark energy). As such it leads to a certain overlap with our previously published works [13][14][15][16][17][18]. To make it easier to read this paper, we found it necessary to go beyond references to our published work and included in the paper some already published results along with yet unpublished results.…”

“…In [16] were incorrect (see [16] and references therein). All these works lose any meaning after renormalization of gravitational Lagrangian by quadratic counterterms off the mass shell.…”

“…This fact makes such works mathematically inconsistent and physically meaningless. In the finite one-loop quantum theory of gravitons presented in [13,16], the incorrect counterterms simply do not arise. In other words, the renormalization procedure (used in all papers known to us) is inapplicable to the quantum theory of gravitons in the one-loop approximation.…”

Quantum Mechanics Allows Setting Initial Conditions at a Cosmological Singularity: Gowdy Model Example

“…It should be noted that the Heisenberg picture for gravity quantization using anticommutative ghost variables was discussed in Ref. [31]. The Schrödinger picture using anticommutative ghost variables has also been developed [32][33][34].…”