Related papers: On quantum corrections to geodesics in de-Sitter s…
The group theoretical approach to the relativistic wave equations in the de Sitter and Anti-de Sitter spaces for spin~0 and 1/2 massive particles is considered. The invariant wave equations which determines the appropriate irreducible…
The discrete Klein-Gordon equation on a two-dimensional square lattice satisfies an $\ell^1 \mapsto \ell^\infty$ dispersive bound with polynomial decay rate $|t|^{-3/4}$. We determine the shape of the light cone for any choice of the mass…
We obtain solutions of the Wheeler-DeWitt equation with positive cosmological constant for a closed universe in the large-volume limit. We argue that this space of solutions provides a complete basis for the Hilbert space of quantum gravity…
The computational analysis of the Cauchy problem for semi-linear Klein-Gordon equations in the de Sitter spacetime is considered. Several simulations are performed to show the time-global behaviors of the solutions of the equations in the…
The recent analysis of quantum cosmology by S. Gielen [1] is extended by discussing the case of dust (in the flat case). The dependence of the Wheeler-DeWitt equation on the operator ordering of the Hamiltonian in the case of a position…
In a suitably chosen essentially unique frame tied to a given observer in a general spacetime, the equation of geodesic deviation can be decomposed into a sum of terms describing specific effects: isotropic (background) motions associated…
This paper deals with the Klein-Gordon equation on the Poincar\'e chart of the 5-dimensional Anti-de Sitter universe. When the mass $\mu$ is larger than $-{1}{4}$, the Cauchy problem is well posed despite the loss of global hyperbolicity…
We formulate the quantum mechanics of the solutions of a Klein-Gordon-type field equation: (\partial_t^2+D)\psi(t)=0, where D is a positive-definite operator acting in a Hilbert space \tilde H. We determine all the positive-definite inner…
We study the decoherence effect of quantum superposition in de Sitter (dS) spacetime due to the presence of the cosmological horizon. Using the algebraic approach of quantum field theory on curved spacetime, we derive the precise expression…
In this paper we will discuss how to localise a quantum wave-packet due to self-gravitating meso-scopic object by taking into account gravitational self-interaction in the Schr\"odinger equation beyond General Relativity. In particular, we…
We consider non-relativistic point-particles coupled to Einstein gravity and their canonical quantization. From the resulting Wheeler-DeWitt wave equation we determine a quantum version of geometrodynamics, where the coupled evolution of…
We obtain the exact solution of the Klein-Gordon equation describing the propagation of a particle in two regions of different constant magnetic field, separated by an infinite plane wall. The continuity of the wave function and of its…
We derive the geodesic equation for point particles propagating in Moyal-type noncommutative spacetimes using a field-theoretic approach based on the quasi-classical limit of the noncommutative Klein-Gordon equation. Starting from a…
A class of radiative solutions of Einstein's field equations with a negative cosmological constant and a pure radiation is investigated. The space-times, which generalize the Defrise solution, represent exact gravitational waves which…
In the present study, Kummer's eigenvalue spectra from a charged spinless particle located at spherical pseudo-dot of the form $r^2+1/r^2$ is reported. Here, it is shown how confluent hypergeometric functions have principal quantum numbers…
Based on an extended time-space symmetry, a cylindrical model of gravitational geometrical dynamics with two time-like extra-dimensions leads to a microscopic geodesic description of the curved space-time. Due to interaction of a Higgs-like…
Utilizing various gauges of the radial coordinate we give a description of static spherically symmetric space-times with point singularity at the center and vacuum outside the singularity. We show that in general relativity (GR) there exist…
We start from the Einstein-Hilbert action for the gravitational field in the presence of a "point particle" source, and cast the action into the corresponding phase space form. The dynamical variables of such a system satisfy the point…
We study the 1D Klein-Gordon equation with variable coefficient nonlinearity. This problem exhibits an interesting resonant interaction between the spatial frequencies of the nonlinear coefficients and the temporal oscillations of the…
A system of generalized coherent states for the de Sitter group obeying Klein-Gordon equation and corresponding to the massive spin zero particles over the de Sitter space is considered. This allows us to construct the quantized scalar…