Related papers: Triangleland. I. Classical dynamics with exchange …
The small angle approximation often fails to explain experimental data, does not even predict if a plane pendulum's period increases or decreases with increasing amplitude. We make a perturbation ansatz for the Conserved Energy Surfaces of…
The spin geometry theorem of Penrose is extended from $SU(2)$ to $E(3)$ (Euclidean) invariant elementary quantum mechanical systems. Using the natural decomposition of the total angular momentum into its spin and orbital parts, the…
A completely Lorentz-invariant Bohmian model has been proposed recently for the case of a system of non-interacting spinless particles, obeying Klein-Gordon equations. It is based on a multi-temporal formalism and on the idea of treating…
We propose a new point of view regarding the problem of time in quantum mechanics, based on the idea of replacing the usual time operator $\mathbf{T}$ with a suitable real-valued function $T$ on the space of physical states. The proper…
The general classical solution of the 3D electromagnetic pp-wave spacetime has been obtained. The relevant line element contains an arbitrary essential function providing an infinite number of in-equivalent geometries as solutions. A…
In the operational approach to general probabilistic theories one distinguishes two spaces, the state space of the "elementary systems" and the physical space in which "laboratory devices" are embedded. Each of those spaces has its own…
The main fundamental principles characterizing the vacuum field structure are formulated, the modeling of the related vacuum medium and charged point particle dynamics by means of devised field theoretic tools are analyzed. The Maxwell…
We show that it is possible to obtain self-consistent and physically acceptable relativistic classical equations of motion for a point-like spin-half particle possessing an electric charge and a magnetic dipole moment, directly from a…
Relativistic correction to the Coulomb interaction is considered for strongly correlated electron orbitals. The atomic representation of the Coulomb-Breit interaction and its physical origin are clarified, to generalize a concept of the…
We apply Feynman's principle, ``The same equations have the same solutions'', to Kepler's problem and show that Newton's dynamics in a properly curved 3-D space is identical with that described by Einstein's theory in the 3-D optical…
We consider classical three-body interactions on a Euclidean line depending on the reciprocal distance of the particles and admitting four functionally independent quadratic in the momenta first integrals. These systems are superseparable…
The results of our study of the motion of a three particle, self-gravitating system in general relativistic lineal gravity is presented for an arbitrary ratio of the particle masses. We derive a canonical expression for the Hamiltonian of…
A unified and fully relativistic treatment of the interaction of the electric and magnetic dipole moments of a particle with the electromagnetic field is given. New forces on the particle due to the combined effect of electric and magnetic…
Using a variational method, we exhibit a surprisingly simple periodic orbit for the newtonian problem of three equal masses in the plane. The orbit has zero angular momentum and a very rich symmetry pattern. Its most surprising feature is…
There are known problems of Lorentz-Dirac equation for moving with acceleration charged particle in classical electrodynamics. The model of extended in one dimension particle is proposed and shown that electromagnetic self-interaction can…
Methods of angular momenta are modified and used to solve some actual problems in quantum mechanics. In particular, we re-derive some known formulas for analytical and numerical calculations of matrix elements of the vector physical…
The purpose of this review is to describe in some detail the mathematical relationship between geometrodynamics and connection dynamics in the context of the classical theories of 2+1 and 3+1 gravity. I analyze the standard Einstein-Hilbert…
The proposed temporal fluctuations model attempt for a unitary vision on gravity, electromagnetism and inertia. On obtain Newton law of gravitation and Coulomb law by starting from simple principles. On obtain too the main results of…
We study a formulation of lattice gravity defined via Euclidean dynamical triangulations (EDT). After fine-tuning a non-trivial local measure term we find evidence that four-dimensional, semi-classical geometries are recovered at long…
We propose a form for the action of a relativistic particle subject to a positional force that is invariant under time reparametrization and therefore allows for a consistent Hamiltonian formulation of the dynamics. This approach can be…