Related papers: Canonical Quantization of (2+1)-Dimensional Gravit…
It is proposed that the paradox of wave-particle duality in quantum mechanics may be resolved using a physical picture analogous to magnetic domains. Within this picture, a quantum particle represents a coherent region of a quantum wave…
The conditions for observation of the particle coordinates, required by logic of the Special Relativity and filtering the quantum field effects, are described. A general relation between the corresponding density of probability and the wave…
We construct a quantum mechanics based on the hypothesis of existing compact extra dimensions for a particle that wants to detect it. By introducing a probability function, we express the transition of particle to the extra 2d window. The…
We derive the Gauss-Codazzi equation in the holonomy and plane-angle representations and we use the result to write a Gauss-Codazzi equation for a discrete (2+1)-dimensional manifold, triangulated by isosceles tetrahedra. This allows us to…
The question whether gravitational waves are quantised or not can in principle be answered by the help of correlation measurements. If the gravitational waves are quantised and they are generated by the change of the background metrics then…
The quantum mechanics description of a physical object stretched in space and stable in time from the relativistic space-time properties point of view, introduced in special theory of relativity, is considered and analysed. The mathematical…
In this work, we study the relativistic quantum kinetic equations in 2+1 dimensions from Wigner function formalism by carrying out a systematic semi-classical expansion up to $\hbar$ order. The derived equations allow us to explore…
Real world quantum systems are open to perpetual influence from the wider environment. Quantum gravitational fluctuations provide a most fundamental source of the environmental influence through their universal interactions with all forms…
We perform quantization of a model in which gravity is coupled to a circular dust shell in 2+1 spacetime dimensions. Canonical analysis shows that momentum space of this model is ADS^2-space, and the global chart for it is provided by the…
A key challenge for many quantum gravity approaches is to construct states that describe smooth geometries on large scales. Here we define a family of $(2+1)$-dimensional quantum gravity states which arise from curvature excitations…
Canonical methods allow the derivation of effective gravitational actions from the behavior of space-time deformations reflecting general covariance. With quantum effects, the deformations and correspondingly the effective actions change,…
The paper concerns the fictitious entanglement of the so-called ``singularities'' in problems, pertaining to quantum gravity, due, in point of fact, to the way we try to employ, in that context, differential geometry, the latter being…
The geometry of the classical phase space C of a finite number of degrees of freedom determines the possible duality symmetries of the corresponding quantum mechanics. Under duality we understand the relativity of the notion of a quantum…
General relativity and its cosmological solution predicts the existence of tensor modes of perturbations evolving on top of our Friedman-Lema\^itre-Robertson-Walker expanding Universe. Being gauge invariant and not necessarily coupled to…
Exactly soluble models can serve as excellent tools to explore conceptual issues in non-perturbative quantum gravity. In perturbative approaches, it is only the two radiative modes of the linearized gravitational field that are quantized.…
I address the question whether the wave function in quantum theory exists as a real (ontic) quantity or not. For this purpose, I discuss the essentials of the quantum formalism and emphasize the central role of the superposition principle.…
It is argued that quantum states of geometry, like those of particles, should be coherent on light cones of any size. An exact classical solution, the gravitational shock wave of a relativistic point particle, is used to estimate…
A general formulation of classical relativistic particle mechanics is presented, with an emphasis on the fact that superluminal velocities and nonlocal interactions are compatible with relativity. Then a manifestly relativistic-covariant…
We consider classical and quantum dynamics of a free particle in de Sitter's space-times with different topologies to see what happens to space-time singularities of removable type in quantum theory. We find analytic solution of the…
The effective quantum field theory description of gravity, despite its non-renormalizability, allows for predictions beyond classical general relativity. As we enter the age of gravitational wave astronomy, an important and timely question…