相关论文: Laplace-Runge-Lenz symmetry in general rotationall…
The internal symmetry of composite relativistic systems is discussed. It is demonstrated that Lorentz-Poincar\'e symmetry implies the existence of internal moments associated with the Lorentz boost, which are Laplace-Runge-Lenz (LRL)…
The characteristic feature of the Kepler Problem is the existence of the so-called Laplace--Runge--Lenz vector which enables a very simple discussion of the properties of the orbit for the problem. It is found that there are many classes of…
A countable set of superintegrable quantum mechanical systems is presented which admit the dynamical symmetry with respect to algebra so(4). This algebra is generated by the Laplace-Runge-Lenz vector generalized to the case of arbitrary…
Superintegrable d - dimensional quantum mechanical systems with spin, which admit a generalized Laplace-Runge-Lenz vector are presented. The systems with spins 0, 1/2 and 1 are considered in detail. All these systems are exactly solvable…
Symmetries are essential for a consistent formulation of many quantum systems. In this paper we discuss a previously unnoticed symmetry, which is present for any Lagrangian term that involves $\dot{x}^2$. As a basic model that incorporates…
Scalar, vector and tensor conserved quantities are essential tools in solving different problems in physics and complex, nonlinear differential equations in mathematics. In many guises they enter our understanding of nature: charge, lepton,…
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…
The main point of this paper is to examine a "hidden" dynamical symmetry connected with the conservation of Laplace-Runge-Lenz vector (LRL) in the hydrogen atom problem solved by means of noncommutative quantum mechanics (NCQM). The basic…
The Kepler problem in classical mechanics exhibits a rich structure of conserved quantities, highlighted by the Laplace--Runge--Lenz (LRL) vector. Through Noether's theorem in reverse, the LRL vector gives rise to a corresponding…
We revisit the connection between relativistic orbital precession, the Laplace-Runge-Lenz symmetry, and the $t$-channel discontinuity of scattering amplitudes. Applying this to scalar-tensor theories of gravity, we compute the conservative…
We introduce a type of symmetry breaking and associated order parameter in connection with Laplace-Runge-Lenz vector of Kepler orbit through an extended spatial dimension and Ensemble view. By implementation of a small extra spatial…
In this letter we reconsider the role of Lorentz invariance in the dynamical generation of the observed internal symmetries. We argue that, generally, Lorentz invariance can only be imposed in the sense that all Lorentz non-invariant…
The standard General Relativity results for precession of particle orbits and for bending of null rays are derived as special cases of perturbation of a quantity that is conserved in Newtonian physics, the Runge-Lenz vector. First this…
The existence of the theory of `twisted cotangent bundles' (symplectic groupoids) allows to study classical mechanical systems which are generalized in the sense that their configurations form a Poisson manifold. It is natural to study from…
It is well-known that an electric charge under a uniform magnetic field has a bidimensional motion if its initial position and velocity are perpendicular to this magnetic field. Although some constants of motion, as the energy and angular…
Recent numerical work indicates that the classical motion of positronium in a constant magnetic field does not exhibit chaotic behavior if the system is confined to two dimensions. One would therefore expect this system to possess a second…
It is shown that a nonrelativistic mechanical system involving a general nonrelativistic potential V(|r1-r2|) between point particles at positions r1 and r2 can be extended to a Lagrangian system which is invariant under Lorentz…
The inverse square force law admits a conserved vector that lies in the plane of motion. This vector has been associated with the names of Laplace, Runge, and Lenz, among others. Many workers have explored aspects of the symmetry and…
We study periodic orbits in the spatial rotating Kepler problem from a symplectic-topological perspective. Our first main result provides a complete classification of these orbits via a natural parametrization of the space of Kepler orbits,…
We review the origin of the physical consistency of the Lorentz- Poincar\'e symmetry. We outline seemingly catastrophic physical inconsistencies recently identified for noncanonical-nonunitary generalized theories defined on conventional…