Related papers: Bertrand spacetimes as Kepler/oscillator potential…
A comparative analysis of the Mathisson-Papapetrou and Pomeransky-Khriplovich equations is presented. Motion of spinning particles and their spins in gravitational fields and noninertial frames is considered. The angular velocity of spin…
A celebrated result of Bertrand states that the only central force potentials on the plane with the property that all bounded orbits are periodic are the Kepler potential and the potential of the harmonic oscillator. In this paper, we…
We derive a systematic treatment of one-loop effective potentials for interacting scalar fields in curved spacetimes, providing a general formula valid in arbitrary geometries and explicit results for de Sitter and anti-de Sitter…
In this contribution, we discuss three situations in which complete integrability of a three dimensional classical system and its quantum version can be achieved under some conditions. The former is a system with axial symmetry. In the…
We consider two-dimensional harmonic oscillator in the complex Bargmann-Fock-Segal representation with $T^*{\mathbb R}^{2}={\mathbb C}^2$ as classical phase space. We show that the eigenfunctions $\psi_n$ of the quantum Hamiltonian…
Fluctuation terms and higher moments of a quantum state imply corrections to the classical equations of motion that may have implications in early-universe cosmology, for instance in the state-dependent form of effective potentials. In…
We define `third derivative' General Relativity, by promoting the integration measure in Einstein-Hilbert action to be an arbitrary $4$-form field strength. We project out its local fluctuations by coupling it to another $4$-form field…
A nonlinear model of the quantum harmonic oscillator on two-dimensional spaces of constant curvature is exactly solved. This model depends of a parameter $\la$ that is related with the curvature of the space. Firstly the relation with other…
We consider a $(4 + 2k)$ - dimensional Einstein-Gauss-Bonnet model with the cosmological $\Lambda$-term. Exact stable solutions with three constant Hubble-like parameters in this model are obtained. In this case, the multidimensional…
The notion of a classical particle is inferred from Dirac quantum fields on a curved space-time, by an eikonal approximation and a localization hypothesis for amplitudes. This procedure allows to define a semi-classical version of the…
The {\em focal curve} of an immersed smooth curve $\gamma:s\mapsto \gamma(s)$, in Euclidean space $\R^{m+1}$, consists of the centres of its osculating hyperspheres. The focal curve may be parametrised in terms of the Frenet frame of…
We present the case of time-varying cosmological term $\Lambda(t)$. The main idea arises by proposing that as in the cosmological constant case, the scalar potential is identified as $ V(\phi)=2\Lambda$, with $\Lambda$ a constant, this…
Classical macroscopic space-time is pictured in terms of Rydberg states of an underlying discritzed `atomic' quantum geometry at Planck scales. While quantum geometry on such scales involves several very short lived transitions changing…
After presenting various concepts and results concerning the classical Steklov eigenproblem, we focus on analogous problems for time-harmonic Maxwell's equations in a cavity. In this direction, we discuss recent rigorous results concerning…
For the time-space fractional degenerate Keller-Segel equation \begin{equation*} \begin{cases} \partial _{t}^{\beta }u=-(-\Delta )^{\frac{\alpha}{2}}(\rho (v)u),& t>0\\ (-\Delta )^{\frac{\alpha}{2}} v+v=u,& t>0 \end{cases} \end{equation*}…
In the first days of quantum mechanics Dirac pointed out an analogy between the time-dependent coefficients of an expansion of the Schr\"odinger equation and the classical position and momentum variables solving Hamilton's equations. Here…
The necessity of rejecting the numerical model of geometrical extension is postulated on the basis of the idea of identity of space-time and physical vacuum. An attempt is made to define space-time not via the concept of manifold, but via…
A mathematical model is given for the occurrence of preferred orbits and orbital velocities in a Keplerian system. The result can be extended into energies and other properties of physical systems. The values given by the model fit closely…
The action of the quantum mechanical volume operator, introduced in connection with a symmetric representation of the three-body problem and recently recognized to play a fundamental role in discretized quantum gravity models, can be given…
In the context of the teleparallel equivalent of general relativity (TEGR) theory, continues calculations of the total energy and momentum for Kerr-NUT spacetimes using three different methods, the gravitational energy-momentum, the…