Quantum gravity in Heisenberg representation and self-consistent theory of gravitons in macroscopic spacetime

TL;DR

This paper derives the first consistent exact equations for quantum gravity in the Heisenberg representation, enabling calculations of graviton interactions and the quantum evolution of macroscopic spacetime without restrictions on graviton properties.

Contribution

It introduces a mathematically consistent formulation of quantum gravity in the Heisenberg representation and Hamilton gauge, linking path integrals with operator equations and enabling self-consistent macroscopic spacetime modeling.

Findings

Equations are compatible without restrictions on graviton amplitude or wavelength.

Path integral in Hamilton gauge is equivalent to operator quantum gravity equations.

Standard S-matrix results are recovered in the appropriate limit.

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 spacetime 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.