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The Einstein-Hilbert action for general relativity is not well posed in terms of the metric $g_{ab}$ as a dynamical variable. There have been many proposals to obtain an well posed action principle for general relativity, e.g., addition of…

It is shown that certain aspects of gravitation may be described using a relativistic action-at-a-distance formulation. The equations of motion of the model presented are invariant under Lorentz transformations and agree with the equations…

Quantum gravity places entirely new challenges on the formulation of a consistent theory as well as on an extraction of potentially observable effects. Quantum corrections due to the gravitational field are commonly expected to be tiny…

We show how to reliably calculate quantum gravitational corrections to cosmological models using the unique effective action formalism for quantum gravity. Our calculations are model independent and apply to any ultra-violet complete theory…

We give a general expression for the static potential energy of the gravitational interaction of two massive particles, in terms of an invariant vacuum expectation value of the quantized gravitational field. This formula holds for…

The gravitational action is not always additive in the usual sense. We provide a general prescription for the change in action that results when different portions of the boundary of a spacetime are topologically identified. We discuss…

In this we briefly cover the covariant approach to describe inertial forces in general relativity and in particular look at the behaviour of the cumulative drag index for stationary Kerr geometry.

It is shown that the difficulties in formulating the quantum field theory on discrete spacetime appear already in classical dynamics of one degree of freedom on discrete time. The difference equation of motion which maintains a conserved…

Over recent years, a lot of progress has been achieved in understanding of the relationship between localization and transport of energy in essentially nonlinear oscillatory systems. In this paper we are going to demonstrate that the…

We apply QED theory to quantum gravity and find it leads to general relativity in the classical limit. We discuss the implications of the result for the quantum-classical divide. This enables us to relate our result to M-theory.

We perform canonical analysis of new non-relativistic string action that was found recently in [arXiv:2107.00642 [hep-th]]. We also discuss its gauge fixed form.

Based on Lorentz invariance and Born reciprocity invariance, the canonical quantization of Special Relativity (SR) is shown to provide a unified origin for: i) the complex vector space formulation of Quantum Mechanics (QM); ii) the momentum…

I shall discuss some "conditions of possibility" of a quantum theory of gravity, stressing the need for solutions to some of fundamental problems confronting any attempt to apply some method of quantization to the field equations of general…

We face the well-known gyrokinetic problem, which arises in the description of the dynamics of a charged particle subject to fast gyration for the presence of a strong electromagnetic field. The customary approach to gyrokinetic theory,…

We propose a formulation of quantum mechanics in an extended Fock space in which a tensor product structure is applied to time. Subspaces of histories consistent with the dynamics of a particular theory are defined by a direct quantum…

A quantum version of the action principle in a simple covariant dynamical theory of two relativistic particles is formulated. The central object of this new formulation of quantum theory is a stationary eigenvalue of the quantum action.…

General Relativity can be reformulated as a diffeomorphism invariant SU(2) gauge theory. A new action principle for this "pure connection" formulation of GR is described.

We revise the problem of the quantization of relativistic particle, presenting a modified consistent canonical scheme, which allows one not only to include arbitrary backgrounds in the consideration but to get in course of the quantization…

These lecture notes cover some of the theoretical topics associated with cosmic acceleration. Plausible explanations to cosmic acceleration include dark energy, modified gravity and a violation of the Copernican principle. Each of these…

We introduce a new class of nonlocal kinetic equations and nonlocal Fokker-Planck equations associated with an effective generalized thermodynamical formalism. These equations have a rich physical and mathematical structure that can…