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Recently proposed quantization in field theory based on an analogue of Hamiltonian formulation which treats space and time on equal footing (the so-called De Donder-Weyl theory) is applied to General Relativity in metric variables. We…
Finite expressions for the mean value of the stress tensor corresponding to a scalar field with a generalized dispersion relation in a Friedman--Robertson--Walker universe are obtained using adiabatic renormalization. Formally divergent…
We consider the special and general relativistic extensions of the action principle behind the Schr\"odinger equation distinguishing classical and quantum contributions. Postulating a particular quantum correction to the source term in the…
The Einstein equation in D dimensions, if restricted to the class of space-times possessing n = D - 2 commuting hypersurface-orthogonal Killing vectors, can be equivalently written as metric-dilaton gravity in 2 dimensions with n scalar…
Planck units are natural physical scales of mass, length and time, built with the help of the fundamental constants $\hbar, c, G$. The functional role of the constants used for the construction of Planck units is different. If the first two…
A discussion is given of the uncertainty principle in view of the introduction of a Gravitational Planck Constant. The need for such a gravitational constant is shown first. A reduced electromagnetic Planck constant and the analogous…
Recently, a model for an emergent gravity based on $SO(5)$ Yang-Mills action in Euclidian 4-dimensional spacetime was proposed. In this work we provide some 1 and 2-loops computations and show that the model can accommodate suitable…
Following on from two recent papers, here we examine the relationship between Newtonian gravitation and general relativity in more depth. This allows us to define a scalar potential which is just the proper time of the vector potential when…
This paper examines a cosmological model of scale-dependent gravity. The gravitational action is taken to be the Einstein-Hilbert term supplemented with a cosmological constant, where the couplings, $G_k$ and $\Lambda_k$, run with the…
In the standard approach to studying cosmological structure formation, the overall expansion of the Universe is assumed to be homogeneous, with the gravitational effect of inhomogeneities encoded entirely in a Newtonian potential. A topic…
In an ever-expanding spatially closed universe, the fractional change of the volume is the preeminent intrinsic time interval to describe evolution in General Relativity. The expansion of the universe serves as a subsidiary condition which…
The work shows that the associated Einstein like gravity for the Klein-Gordon field shows the spontaneous emergence of the cosmological pressure tensor density (CPTD) that in the classical limit leads to the cosmological constant (CC). Even…
We use our resummed quantum gravity approach to Einstein's general theory of relativity in the context of the Planck scale cosmology formulation of Bonanno and Reuter to estimate the value of the cosmological constant as \rho_\Lambda…
In the 6-dimensional model of warped compactification based on the euclidean AdS Reissner-Nordstrom metric it is possible to escape artificial 4-brane's stress-energy tensor anistropy necessary for fulfillment of Israel junction conditions…
The algebra of polynomials in operators that represent generalized coordinate and momentum and depend on the Planck constant is defined. The Planck constant is treated as the parameter taking values between zero and some nonvanishing $h_0$.…
We extend the three-dimensional noncommutative relations of the positions and momenta operators to those in the four dimension. Using the Bopp shift technique, we give the Heisenberg representation of these noncommutative algebras and endow…
A formula of the renormalized volume of tubes over polalized K\"{a}hler-Einstein manifolds is given in terms of the Einstein constant and the volume of the polarization.
Theories based on General Relativity or Quantum Mechanics have taken a leading position in macroscopic and microscopic Physics, but fail when used in the other extremity. Thus, we try to establish a new structure of united theory based on…
This work completes a serie of two papers devoted to the extension of the fundamental laws of electrodynamics in the context of Fock's nonlinear relativity (FNLR). Indeed, after having established in the previous study the exact…
Two approaches to quantization of Freedman's closed Universe are compared. In the first approach, the Shrodinger's norm of the wave function of Universe is used, and in the second approach, the Klein-Gordon's norm is used. The second one…