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A reference frame consists of: a reference space, a time scale and a spatial metric. The geometric structure induced by these objects in spacetime is developed. The existence of a class of spatial metrics that are rigid, have free mobility…
A labeled metric space is intuitively speaking a metric space together with a special set of points to be understood as the geometric boundary of the space. We study basic properties of a recently introduced labeled Gromov-Hausdorff…
Using the Gitman-Lyakhovich-Tyutin generalization of the Ostrogradsky method for analyzing singular systems, we consider the Hamiltonian formulation of metric and tetrad gravities in two-dimensional Riemannian spacetime treating them as…
A deformation of special relativistic kinematics (possible signal of a theory of quantum gravity at low energies) leads to a modification of the notion of spacetime. At the classical level, this modification is required when one considers a…
In this work we discuss the deformed relativistic wave equations, namely the Klein--Gordon and Dirac equations in a Doubly Special Relativity scenario. We employ what we call a geometric approach, based on the geometry of a curved momentum…
Based on some important properties of $dS$ space, we present a Beltrami model ${\cal B}_\Lambda$ that may shed light on the observable puzzle of $dS$ space and the paradox between the special relativity principle and cosmological principle.…
We connect the algebraic geometry and representation theory associated to Freudenthal's magic square. We give unified geometric descriptions of several classes of orbit closures, describing their hyperplane sections and desingularizations,…
The space-time length R between a moving source and the observation point is calculated in order to substitute with it the spatial distance D, normally used in the Newton's law of gravitation, as well as in any inverse-square-law.…
We derive new solutions of the Schr\"odinger equation which describe the motion of particles in the Penning trap. These solutions are direct counterparts of classical orbits. They are obtained by injection of classical trajectories into the…
In this paper we prove two general results related to Marstrand's projection theorem in a quite general formulation over separable metric spaces under a suitable transversality hypothesis (the "projections" are in principle only measurable)…
Limits and characteristic periods of variations in orbital elements of planets were studied by numerical integration of equations of motion. Interrelations between the characteristic periods of variations in orbital elements of some planets…
Combining gravity with quantum theory is still work in progress. On the one hand, classical gravity, is the geometry of space-time determined by the energy-momentum tensor of matter and the resulting nonlinear equations; on the other hand,…
We treat the circular and elliptic restricted three-body problems in inertial frames as periodically forced Kepler problems with additional singularities and explain that in this setting the main result of [4] is applicable. This guarantees…
We study joint measurability of quantum observables in open systems governed by a master equation of Lindblad form. We briefly review the historical perspective of open systems and conceptual aspects of quantum measurements, focusing…
The increasing number and variety of extrasolar planets illustrates the importance of characterizing planetary perturbations. Planetary orbits are typically described by physically intuitive orbital elements. Here, we explicitly express the…
In many robotics applications, it is necessary to compute not only the distance between the robot and the environment, but also its derivative - for example, when using control barrier functions. However, since the traditional Euclidean…
We propose a mathematical model of quantum spacetime as an infinite-dimensional manifold locally homeomorphic to an appropriate Schwartz space. This extends and unifies both the standard function space construction of quantum mechanics and…
In a classical Hamiltonian theory with second class constraints the phase space functions on the constraint surface are observables. We give general formulas for extended observables, which are expressions representing the observables in…
Some of the most outstanding questions in the field of gravitation and geometry remain unsolved as a result of our limited understanding of the global structure of the spacetime geometry and the role played by global spacetime…
A small time delay between interactions, which has previously been shown to remove divergences from QED, is used to show that, if spacetime geometry is emergent from particle interactions in the manner suggested by Bondi, then Minkowski…