Related papers: A note on the action-angle variables for the ratio…
We investigate the relation between the local variables of a discrete integrable lattice system and the corresponding separation variables, derived from the associated spectral curve. In particular, we have shown how the inverse…
We perform the canonical analysis of the Holst action for general relativity with a cosmological constant without introducing second-class constraints. Our approach consists in identifying the dynamical and nondynamical parts of the…
- We have suggested using the action-angle variables for the study of a (quasi)particle in quantum ring. We have presented the action-angle variables for three two-dimensional singular oscillator systems - We have suggested a procedure of…
For the Toda lattice and the Holt system we consider properties of canonical transformations of the extended phase space, which preserve integrability. The separated variables are invariant under change of the time. On the other hand,…
In this paper, we investigate solvable structures associated to Hamiltonian equations. For a completely integrable Hamiltonian system with $n$ degrees of freedom, we construct a canonical solvable structure consisting of $2n$ Hamiltonian…
Quantum versions of cylindric phase space, like for the motion of a particle on the circle, are obtained through different families of coherent states. The latter are built from various probability distributions of the action variable. The…
A new ansatz is presented for a Lax pair describing systems of particles on the line interacting via (possibly nonsymmetric) pairwise forces. Particular cases of this yield the known Lax pairs for the Calogero-Moser and Toda systems, as…
We discuss some paradoxes arising due to the gauge-dependence of canonical variables in mechanics.
The equivalence between the N-particle Calogero-Moser systems and the integrable sl(N,$\mathbb{C}$)-tops is shown. New rational and trigonometric classical Lax operators for these systems are found. Relations with new solutions of the…
The Poisson brackets for the scattering data of the Camassa-Holm equation are computed. Consequently, the action-angle variables are expressed in terms of the scattering data.
We present an elementary discussion of the Calogero-Moser model. This gives us an opportunity to illustrate basic concepts of the dynamical integrable models. Some ideas are also presented regarding interconnections between integrable…
The aim of this paper is to introduce and analyze a new gauge symmetry that appears in complex holomorphic systems. This symmetry allow us to project the system, using different gauge conditions, to several real systems which are connect by…
The essentially unique reduction of the Euler-Poinsot problem may be performed in different sets of variables. Action-angle variables are usually preferred because of their suitability for approaching perturbed rigid-body motion. But they…
In this paper we demonstrate that there exists a close relationship between quasi-exactly solvable quantum models and two special classes of classical dynamical systems. One of these systems can be considered a natural generalization of the…
For a time-dependent classical quadratic oscillator we introduce pairs of real and complex invariants that are linear in position and momentum. Each pair of invariants realize explicitly a canonical transformation from the phase space to…
New variables of separation for few integrable systems on the two-dimensional sphere with higher order integrals of motion are considered in detail. We explicitly describe canonical transformations of initial physical variables to the…
The complete variables separation is given for one Hamiltonian system with two degrees of freedom arising in the motion of the Kowalevski type top in two constant fields.
A two-dimensional integrable system being a deformation of the rational Calogero-Moser system is constructed via the symplectic reduction, performed with respect to the Sklyanin algebra action. We explicitly resolve the respective classical…
Calogero-Moser systems can be generalized for any root system (including the non-crystallographic cases). The algebraic linearization of the generalized Calogero-Moser systems and of their quadratic (resp. quartic) perturbations are…
The classical and quantum aspects of planar Coulomb interactions have been studied in detail. In the classical scenario, Action Angle Variables are introduced to handle relativistic corrections, in the scheme of time-independent…