Related papers: Carter Constant and Superintegrability
We discuss constants of motion of a particle under an external field in a curved spacetime, taking into account the Hamiltonian constraint which arises from reparametrization invariance of the particle orbit. As the necessary and sufficient…
We develop new constructions of 2D classical and quantum superintegrable Hamiltonians allowing separation of variables in Cartesian coordinates. In classical mechanics we start from two functions on a one-dimensional phase space, a natural…
We identify a new superintegrable Hamiltonian in 3 degrees of freedom, obtained as a reduction of pure Keplerian motion in 6 dimensions. The new Hamiltonian is a generalization of the Keplerian one, and has the familiar 1/r potential with…
A new intrinsically-relativistic kinetic mechanism for generation of non-isotropic relativistic kinetic equilibria in collisionless N-body systems is pointed out. The theory is developed in the framework of the covariant Vlasov statistical…
We consider here the coexistence of first- and third-order integrals of motion in two dimensional classical and quantum mechanics. We find explicitly all potentials that admit such integrals, and all their integrals. Quantum superintegrable…
We study some symmetry and integrability properties of four-dimensional Einstein-Maxwell gravity with nonvanishing cosmological constant in the presence of Killing vectors. First of all, we consider stationary spacetimes, which lead, after…
The superintegrability of a rational harmonic oscillator (non-central harmonic oscillator with rational ratio of frequencies) with non-linear "centrifugal" terms is studied. In the first part, the system is directly studied in the Euclidean…
The Lie-Poisson algebra so(N+1) and some of its contractions are used to construct a family of superintegrable Hamiltonians on the ND spherical, Euclidean, hyperbolic, Minkowskian and (anti-)de Sitter spaces. We firstly present a…
The motion of test particles in stationary axisymmetric gravitational fields is generally nonintegrable unless a nontrivial constant of motion, in addition to energy and angular momentum along the symmetry axis, exists. The Carter constant…
We develop a systematic framework for formulating and solving the conditions that lead to separability in stationary, axisymmetric spacetimes in the presence of matter fields. Guided by Carter's metric form, we introduce a general…
We investigate a quantum nonrelativistic system describing the interaction of two particles with spin 1/2 and spin 0, respectively. We assume that the Hamiltonian is rotationally invariant and parity conserving and identify all such systems…
This article is a contribution to the study of superintegrable Hamiltonian systems with magnetic fields on the three-dimensional Euclidean space $\mathbb{E}_3$ in quantum mechanics. In contrast to the growing interest in complex…
The correspondence between the integrability of classical mechanical systems and their quantum counterparts is not a 1-1, although some close correspondencies exist. If a classical mechanical system is integrable with invariants that are…
A discussion of the number of degrees of freedom, and their dynamical properties, in higher derivative gravitational theories is presented. The complete non-linear sigma model for these degrees of freedom is exhibited using the method of…
In this paper we explore general conditions which guarantee that the geodesic flow on a 2-dimensional manifold with indefinite signature is locally separable. This is equivalent to showing that a 2-dimensional natural Hamiltonian system on…
Superintegrable systems are a class of physical systems which possess more conserved quantities than their degrees of freedom. The study of these systems has a long history and continues to attract significant international attention. This…
In this paper, we derive a nonseparable quantum superintegrable system in 2D real Euclidean space. The Hamiltonian admits no second order integrals of motion but does admit one third and one fourth order integral. We also obtain a classical…
The R-matrix formalism for the construction of integrable systems with infinitely many degrees of freedom is reviewed. Its application to Poisson, noncommutative and loop algebras as well as central extension procedure are presented. The…
We consider a possibility that the cosmological constant may not be a constant, but a free thermodynamical variable. To this end we construct a microscopic model of a spacelike two-sphere just inside of the cosmological horizon of the de…
We discuss the properties of superintegrable Hamiltonian systems, in particular those that admit separation of variables in cartesian coordinates. We show that the superintegrability of such potentials is equivalent to the isochronicity of…