Related papers: A Note on the Passing Time of the Spherical Kepler…
Isochrone potentials, as defined by Michel H\'enon in the fifties, are spherically symmetric potentials within which a particle orbits with a radial period that is independent of its angular momentum. Isochrone potentials encompass the…
Pulsars are remarkably precise "celestial clocks" that can be used to explore many different aspects of physics and astrophysics. In this article I give a brief summary of pulsar properties and describe some of the applications of pulsar…
We give an up-to-date overview of geometric and topological properties of cosymplectic and coKaehler manifolds. We also mention some of their applications to time-dependent mechanics.
We review a few useful concepts about polarization measurements in the quantum domain. Using a perfectly general formalism, we show how to build the quantum counterpart of some classical quantities like Stokes parameters and Mueller…
As a first step in exploring time-periodic solutions of the Einstein equations with a negative cosmological constant, we study the cubic conformal wave equation on the Einstein cylinder. Using a combination of numerical and perturbative…
We have studied various classical solutions in $R^2$ cosmology. Especially we have obtained general classical solutions in pure $R^2$\ cosmology. Even in the quantum theory, we can solve the Wheeler-DeWitt equation in pure $R^2$\ cosmology…
Discussion of some aspects of the concept of time for a general audience: nature of time, A- and B-series, time in physics, the "now", measurement of time, definition of time units, time's arrow, relativity of time, relativity of…
Quantum mechanical WKB-method is elaborated for the known quantum Kepler problem in curved 3-space models Euclide, Riemann and Lobachevsky in the framework of the complex variable function theory. Generalized Schr\"{o}dinger, Klein-Fock…
Spherical field theory is a new non-perturbative method for studying quantum field theories. It uses the spherical partial wave expansion to reduce a general d-dimensional Euclidean field theory into a set of coupled one-dimensional…
In this paper, we derive some interesting symmetric properties for the geenralized Euler numbers and polynomials.
A basic problem in quantizing a field in curved space is the decomposition of the classical modes in positive and negative frequency. The decomposition is equivalent to a choice of a complex structure in the space of classical solutions. In…
We discuss the notion of quantum mechanical coherence in its connection with time evolution and stationarity. The transition from coherence to decoherence is examined in terms of an equation for the time dependence of the density matrix. It…
This is a philosophy paper rather than mathematical physics work. I will publish it in some other place.
In this article we present some recent results on identifying correctly the relativistic multipole moments of numerically constructed spacetimes, and the consequences that this correction has on searching for appropriate analytic spacetimes…
We cautiously reanalyze some easily confused notions on particle horizon problem in this paper and then we give a new answer to the particle horizon problem. This answer is independent of physics plunging into Planck time.
In this final piecemeal treatment of local Problem of Time facets, and underlying Background Independence aspects, we first reconsider the ten local facets and aspects considered so far at the quantum level. This is essential both to…
We point out how some recent developments in the theory of constant scalar curvature K\"ahler metrics can be used to clarify the existence issue for such metrics in the special case of geometrically ruled complex surfaces.
A brief report on recent work on the sphere-packing problem.
The inverse relationship between energy and time is as familiar as Planck's constant. From the point of view of a system with many states, perhaps a better representation of the system is a vector of characteristic times (one per state) for…
The Kepler problem concerns a point particle in an attractive inverse square force. After a brief review of the classical and quantum versions of this problem, focused on their hidden $\text{SU}(2) \times \text{SU}(2)$ symmetry, we discuss…