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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.
Using the instanton representation method, we re-construct graviton solutions about DeSitter spacetime. We have used this example as a testing arena to expose the internal structure of the method and to establish that it works for known solutions. Th
The Averaged Null Energy Condition (ANEC) states that the integral along a complete null geodesic of the projection of the stress-energy tensor onto the tangent vector to the geodesic cannot be negative. ANEC can be used to rule out spacetimes with e
Small violations of spacetime symmetries have recently been identified as promising Planck-scale signals. This talk reviews how such violations can arise in various approaches to quantum gravity, how the emergent low-energy effects can be described w
This review summarizes the current status of the energy conditions in general relativity and quantum field theory. We provide a historical review and a summary of technical results and applications, complemented with a few new derivations and discuss
We formulate Eddingtons affine gravity in a spacetime which is immersed in a larger eight dimensional space endowed with a hypercomplex structure. The dynamical equation of the first immersed Ricci-type tensor leads to gravitational field equations w