相关论文: Illustrating Dynamical Symmetries in Classical Mec…

Besides the well known scalar invariants, there exist also vectorial invariants in the realm of special relativity. It is shown that the three-vector $\left(\frac{d\vec{p}}{dt}\right)_{\parallel…

This paper expounds the relations between continuous symmetries and conserved quantities, i.e. Noether's ``first theorem'', in both the Lagrangian and Hamiltonian frameworks for classical mechanics. This illustrates one of mechanics' grand…

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…

We study the most general form of a three dimensional classical integrable system with axial symmetry and invariant under the axis reflection. We assume that the three constants of motion are the Hamiltonian, $H$, with the standard form of…

We present a useful proposition for discovering extended Laplace-Runge-Lentz vectors of certain quantum mechanical systems. We propose a new family of superintegrable systems and construct their integrals of motion. We solve these systems…

Non-relativistic conformally invariant systems in a rotating cosmic string (conical) spacetime are analyzed at the classical and quantum levels by means of the gravitoelectromagnetic interpretation of the background. Solutions of the…

It is natural to investigate if the quantization of an integrable or superintegrable classical Hamiltonian systems is still integrable or superintegrable. We study here this problem in the case of natural Hamiltonians with constants of…

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…

We first consider the Lagrangian formulation of general relativity for perturbations with respect to a background spacetime. We show that by combining Noether's method with Belinfante's "symmetrization'' procedure we obtain conserved…

For each simple euclidean Jordan algebra $V$ of rank $\rho$ and degree $\delta$, we introduce a family of classical dynamic problems. These dynamical problems all share the characteristic features of the Kepler problem for planetary…

This paper presents a generalisation of Sylvester's law of inertia to real non-degenerate quadratic forms on a fixed real vector bundle over a connected locally connected paracompact Hausdorff space. By interpreting the classical inertia as…

The problem of Kepler dynamics on a conformable Poisson manifold is addressed. The Hamiltonian function is defined and the related Hamiltonian vector field governing the dynamics is derived, which leads to a modified Newton second law.…

For the general central force equations of motion in $n>1$ dimensions, a complete set of $2n$ first integrals is derived in an explicit algorithmic way without the use of dynamical symmetries or Noether's theorem. The derivation uses the…

In this work we have investigated some properties of classical phase-space with symplectic structures consistent, at the classical level, with two noncommutative (NC) algebras: the Doplicher-Fredenhagen-Roberts algebraic relations and the…

We report here the existence of Ermanno-Bernoulli type invariants for the Manev model dynamics which may be viewed upon as remnants of Laplace-Runge-Lenz vector whose conservation is characteristic of the Kepler model. If the orbits are…

The basic work of Zaslavskii et al showed that the classical non-relativistic electromagnetically kicked oscillator can be cast into the form of an iterative map on the phase space; the resulting evolution contains a stochastic flow to…

A correspondence is established between measure-preserving, ergodic dynamics of a classical harmonic oscillator and a quantum mechanical gauge theory on two-dimensional Minkowski space. This correspondence is realized through an isometric…

We define a new dynamical variable, the relative existence e, in terms of space and time. Taking it as a generalized positional coordinate, we show that for conservative systems the canonically conjugated momentum is identified as the…

We construct a three-dimensional superconformal quantum mechanics (and its associated de Alfaro-Fubini-Furlan deformed oscillator) possessing an $sl(2|1)$ dynamical symmetry. At a coupling parameter $\beta\neq 0$ the Hamiltonian contains a…

The covariant canonical transformation theory applied to the relativistic Hamiltonian theory of classical matter fields in dynamical space-time yields a novel (first order) gauge field theory of gravitation. The emerging field equations…