Related papers: A Curious Use of Extra Dimension in Classical Mech…

The motion of a classical test particle moving on a 4-dimensional brane embedded in an $n$-dimensional bulk is studied in which the brane is allowed to fluctuate along the extra dimensions. It is shown that these fluctuations produce three…

An analysis of classical mechanics in a complex extension of phase space shows that a particle in such a space can behave in a way redolant of quantum mechanics; additional degrees of freedom permit 'tunnelling' without recourse to…

All objects in 4D spacetime may in principle travel on null paths in a 5D mani-fold. We use this, together with a change in the extra coordinate and the signature of the metric, to construct a simple model of a classical universe and a…

Motion of a classical particle in 3-dimensional Lobachevsky and Riemann spaces is studied in the presence of an external magnetic field which is analogous to a constant uniform magnetic field in Euclidean space. In both cases three…

We construct a quantum mechanics based on the hypothesis of existing compact extra dimensions for a particle that wants to detect it. By introducing a probability function, we express the transition of particle to the extra 2d window. The…

Extra dimensions are introduced: 3 in Classical Mechanics and 6 in Relativistic Mechanics, which represent orientations, resulting from rotations, of a particle, described by quaternions, and leading to a 7-dimensional, respectively…

The possibility that spacetime is extended beyond the familiar 3+1-dimensions has intrigued physicists for a century. Indeed, the consequences of a dimensionally richer spacetime would be profound. Recently, new theories with higher…

Modified Newtonian dynamics can be considered as an effect derived from a squeezable extra dimension space. The third law of Newtonian dynamics can be managed to remain valid in the 5-space. The critical acceleration parameter $a_0$ appears…

In this study, we explore the field of physics through the lens of fractional dimensionality. We propose that space is not confined to integer dimensions alone, but can also be understood as a superposition of spaces that exist between…

We consider an inverse variational problem for the lines of constant curvature in (pseudo-)Euclidean two-, three-, and four-dimensional spaces. The accumulated results are physically meaningful in the case of relativistic mechanics of…

We consider the motion of a classical particle under the influence of a random potential on R^d, in particular the distribution of asymptotic velocities and the question of ergodicity of time evolution.

Extra-dimensions are a common topic in popular descriptions of theoretical physics with which undergraduate student most often have no contact in physics courses. This paper shows how students could be introduced to this topic by presenting…

A superintegrable system is, roughly speaking, a system that allows more integrals of motion than degrees of freedom. This review is devoted to finite dimensional classical and quantum superintegrable systems with scalar potentials and…

We derive the path integral action for a particle moving in three dimensional fuzzy space. From this we extract the classical equations of motion. These equations have rather surprising and unconventional features: They predict a cut-off in…

Replacing 4D Minkowski space by 5D canonical space leads to a clearer derivation of the main features of wave mechanics, including the wave function and the velocity of de Broglie waves. Recent tests of wave-particle duality could be…

We study the long time motion of fast particles moving through time-dependent random force fields with correlations that decay rapidly in space, but not necessarily in time. The time dependence of the averaged kinetic energy and…

Euclidean dilaton gravity in two dimensions is studied exploiting its representation as a complexified first order gravity model. All local classical solutions are obtained. A global discussion reveals that for a given model only a…

In this paper we give examples of applications of general methods of quantization by symmetrization of classical integrable systems, which have been illustrated in two previous works by the same authors. We consider two classes of systems…

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…

Although cosmic expansion at very small distances is usually dismissed as entirely inconsequential, it appears that these extraordinarily small effects may in fact have a real and significant influence on our world. Calculations suggest…