Related papers: Quantum Newtonian cosmology and the biconfluent He…
We show that a polynomial H(N) of degree N of a harmonic oscillator hamiltonian allows us to devise a fully solvable continuous quantum system for which the first N discrete energy eigenvalues can be chosen at will. In general such a choice…
The particle in an expanding/contracting 1-dimension box is revisited in action-angle like variables with direct thermodynamic interpretation. An angle dependent potential is proposed accurately describing the mechanical behavior while also…
We discuss the possibility of a dynamical solution to the cosmological constant problem in the contaxt of six-dimensional Einstein-Maxwell theory. A definite answer requires an understanding of the full bulk cosmology in the early universe,…
We formulate an approach to quantum gravity, called the ring paradigm. Gravity is mediated superluminally, and the graviton is described as a phonon on the grid of matter in the Universe. This theory has very interesting applications to…
Building upon our recently established correspondence between quantum cosmology and the hydrogen atom [1], we investigate the specific sector of a negative cosmological constant ($\Lambda < 0$) in a flat FLRW universe with dust. While the…
The harmonic Lagrange top is the Lagrange top plus a quadratic (harmonic) potential term. We describe the top in the space fixed frame using a global description with a Poisson structure on $T^*S^3$. This global description naturally leads…
We present a quantization of unimodular gravity in the connection representation for a homogeneous, isotropic, and spatially flat cosmological model without matter. In this model, the wave function is governed by a Schr\"odinger-type…
It is shown that a class of approximate resonance solutions in the three-body problem under the Newtonian gravitational force are equivalent to quantized solutions of a modified Schr\"odinger equation for a wide range of masses that…
The Heisenberg equations of motion for a quantum particle of mass $m$ are deduced from the infinitesimal qr-number equations of motion for the particle. The infinitesimal qr-number equations, and hence the standard quantum mechanical…
The hypothesis is proposed that under the approximation that the quantum equations of motion reduce to the classical ones, the quantum vacuum also reduces to the classical vacuum--the empty space. The vacuum energy of QED is studied under…
We generalize the well-known Bonnor-Melvin solution of the Einstein-Maxwell equations to the case of a non-vanishing cosmological constant. The spacetime is again cylindrically symmetric and static but, unlike the original solution, it…
We study quantum cosmology with conformal matter comprising a perfect radiation fluid and a number of conformally coupled scalar fields. Focusing initially on the collective coordinates (minisuperspace) associated with homogeneous,…
We present first-order post-Newtonian (1PN) approximations of a general imperfect fluid and of an axion as a coherently oscillating massive scalar field, both in the cosmological context. For the axion, using the Klein transformation and…
An introduction to solutions of the Einstein equations defining cosmological models with accelerated expansion is given. Connections between mathematical and physical issues are explored. Theorems which have been proved for solutions with…
The existence of a simple spherically symmetric and static solution of the Einstein equations in the presence of a cosmological constant vanishing outside a definite value of the radial distance is investigated. A particular succession of…
We compute the running of the cosmological constant and Newton's constant taking into account the effect of quantum fields with any spin between 0 and 2. We find that Newton's constant does not vary appreciably but the cosmological constant…
The analysis of the Helmholtz equation is shown to lead to an exact Hamiltonian system of equations describing in terms of ray trajectories a very wide family of wave-like phenomena (including diffraction and interference) going much beyond…
Einstein-Hilbert action is supplemented by Gauss-Bonnet squared term, its phase-space structure is constructed and canonical quantization is performed. Resolution of a contradiction that emerges in the process, requires the presence of…
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 correct quantum description for a curvature squared term in the action can be obtained by casting the action in the canonical form with the introduction of a variable which is the negative of the first derivative of the field variable…