Related papers: Constrained Dynamics on an Ellipse
This study investigates the different novel forms of the dynamical equations of a particle orbiting a rotating asteroid and the effective potential, the Jacobi integral, etc. on different manifolds. Nine new forms of the dynamical equations…
After the short survey of the Klein Paradox in 3-dimensional relativistic equations, we present a detailed consideration of Dirac modified equation, which follows by one particle infinite overweighting in Salpeter Equation. It is shown,…
We study the dynamics of a one-dimensional classical particle in a space and time dependent potential with randomly chosen parameters. The focus of this work is a quasi-periodic potential, which only includes a finite number of Fourier…
The Dirac quantization of a 2+1 dimensional bubble is performed. The bubble consists of a string forming a boundary between two regions of space-time with distinct geometries. The ADM constraints are solved and the coupling to the string is…
We have recently presented an extension of the standard variational calculus to include the presence of deformed derivatives in the Lagrangian of a system of particles and in the Lagrangian density of field-theoretic models. Classical…
We consider a second degree algebraic curve describing a general conic constraint imposed on the motion of a massive spinless particle. The problem is trivial at classical level but becomes involved and interesting in its quantum…
Differential constraints compatible with the linearized equations of partial differential equations are examined. Recursion operators are obtained by integrating the differential constraints.
The Dirac procedure for dealing with constraints is applied to the quantization of gauge theories on the light front. The light cone gauge is used in conjunction with the first class constraints that arise and the resulting Dirac brackets…
The Dirac equation is a cornerstone in the history of physics, merging successfully quantum mechanics with special relativity, providing a natural description of the electron spin and predicting the existence of anti-matter. Furthermore, it…
The classical dynamics of a particle that is driven by a rapidly oscillating potential (with frequency $\omega$) is studied. The motion is separated into a slow part and a fast part that oscillates around the slow part. The motion of the…
The present work focuses on the study of the renowned Collatz conjecture, also known as the $3x +1$ problem. The distinguished analysis approach lies on the dynamics of an iterative map in binary form. A new estimation of the enlargement of…
Quantum Dirac constraints in generic constrained system are solved by directly calculating in the one-loop approximation the path integral with relativistic gauge fixing procedure. The calculations are based on the reduction algorithms for…
The formalism of Operational Dynamical Modeling [Phys. Rev. Lett. {\bf 109}, 190403 (2012)] is employed to analyze dynamics of spin half relativistic particles. We arrive at the Dirac equation from specially constructed relativistic…
Exact solutions of the Dirac equation, a system of four partial differential equations, are rare. The vast majority of them are for highly symmetric stationary systems. Moreover, only a handful of solutions for time dependent dynamics…
In the present contribution we propose a gedankenexperiment in which the restriction of rational values on the velocities emerges as a necessary condition from Classical Electromagnetism and Quantum Mechanics. This restriction is shown to…
We observe that a wide class of higher-derivative systems admits a bounded integral of motion that ensures the classical stability of dynamics, while the canonical energy is unbounded. We use the concept of a Lagrange anchor to demonstrate…
Some recent results concerning a particle confined in a one-dimensional box with moving walls are briefly reviewed. By exploiting the same techniques used for the 1D problem, we investigate the behavior of a quantum particle confined in a…
The Dirac equation, usually obtained by `quantizing' a classical stochastic model is here obtained directly within classical statistical mechanics. The special underlying space-time geometry of the random walk replaces the missing analytic…
In this work, Schr\"odinger and Dirac equations will be examined in geometries that confine the particles to hypersurfaces. For this purpose, two methods will be considered. The first method is the thin layer method which relies on explicit…
The $n$ integrals in involution for the motion on the $n$-dimensional ellipsoid under the influence of a harmonic force are explicitly found. The classical separation of variables is given by the inverse momentum map. In the quantum case…