2011/08/31 by Grigory Vereshkov, Leonid Marochnik · 1 citation
Mathematics · Physics and Astronomy · #Canonical quantum gravity #Cosmology and Gravitation Theories #Euclidean quantum gravity #Gravitation #Graviton #Hořava–Lifshitz gravity #Linearized gravity #Loop quantum gravity #Noncommutative and Quantum Gravity Theories #Quantization (signal processing) #Quantum Electrodynamics and Casimir Effect #Quantum gravity #Spin foam #gr-qc #math-ph #math.MP
paper · pdf · doi:10.4236/jmp.2013.42039
published as J. Mod. Phys. 4, 285-297 (2013) · 15 pages; v2: Expanded explanation of the reasons why the vast majority of papers on the quantum theory of gravitons published in 1977-2008 is erroneous
openalex publication_date 2013/01/01 · arxiv created 2013/03/05 · arxiv updated 2013/03/06 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
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.