相关论文: New compact forms of the trigonometric Ruijsenaars…
We extend the quantum-classical duality to the trigonometric (hyperbolic) case. The duality establishes an explicit relationship between the classical N-body trigonometric Ruijsenaars-Schneider model and the inhomogeneous twisted XXZ spin…
We suggest a Hamiltonian formulation for the spin Ruijsenaars-Schneider system in the trigonometric case. Within this interpretation, the phase space is obtained by a quasi-Hamiltonian reduction performed on (the cotangent bundle to) a…
We explain that the action-angle duality between the rational Ruijsenaars-Schneider and hyperbolic Sutherland systems implies immediately the maximal superintegrability of these many-body systems. We also present a new direct proof of the…
The Hamiltonian structure of spin generalization of the rational Ruijsenaars-Schneider model is found by using the Hamiltonian reduction technique. It is shown that the model possesses the current algebra symmetry. The possibility of…
The C. Neumann system describes a particle on the sphere S^n under the influence of a potential that is a quadratic form. We study the case that the quadratic form has l+1 distinct eigenvalues with multiplicity. Each group of m_\sigma equal…
We consider three 'classical doubles' of any semisimple, connected and simply connected compact Lie group $G$: the cotangent bundle, the Heisenberg double and the internally fused quasi-Poisson double. On each double we identify a pair of…
We study Hamiltonian reductions of the free geodesic motion on a non-compact simple Lie group using as reduction group the direct product of a maximal compact subgroup and the fixed point subgroup of an arbitrary involution commuting with…
Supersymmetry (SUSY) of Hamiltonian dictates double degeneracy between a pair of superpartners (SPs) transformed by supercharge, except at zero energy where modes remain unpaired in many cases. Here we explore a SUSY of complete isospectrum…
We consider two families of commuting Hamiltonians on the cotangent bundle of the group GL(n,C), and show that upon an appropriate single symplectic reduction they descend to the spectral invariants of the hyperbolic Sutherland and of the…
An integrable supersymmetric generalization of the trigonometric Ruijsenaars-Schneider model is presented whose symmetry algebra includes the super Poincar\'e algebra. Moreover, its Hamiltonian is showed to be diagonalized by the recently…
We study multiplicative quiver varieties associated to specific extensions of cyclic quivers with $m\geq 2$ vertices. Their global Poisson structure is characterised by quasi-Hamiltonian algebras related to these quivers, which were studied…
In this paper, we prove that a two-dimensional self-shrinker, homeomorphic to the sphere, immersed in the three dimensional Euclidean space is a round sphere, provided its mean curvature and the norm of its position vector have an upper…
We demonstrate that the symmetric elliptic polynomials $E_\lambda(x)$ originally discovered in the study of generalized Noumi-Shiraishi functions are eigenfunctions of the elliptic Ruijsenaars-Schneider (eRS) Hamiltonians that act on the…
A deformation of the classical trigonometric BC(n) Sutherland system is derived via Hamiltonian reduction of the Heisenberg double of SU(2n). We apply a natural Poisson-Lie analogue of the Kazhdan-Kostant-Sternberg type reduction of the…
The structure of the reduced phase space arising in the Hamiltonian reduction of the phase space corresponding to a free particle motion on the group ${\rm SL}(2, {\Bbb R})$ is investigated. The considered reduction is based on the…
It has been shown that, by adding an extra free field that decouples from the dynamics, one can construct actions for interacting 2n-form fields with self-dual field strengths in 4n+2 dimensions. In this paper we analyze canonical…
We formulate the problem of finding self-dual Hamiltonians (associated with integrable systems) as deformations of free systems given on various symplectic manifolds and discuss several known explicit examples, including recently found…
It is shown that in every dimension n=3j+2, j=1,2,3,..., there exist compact pseudo-Riemannian manifolds with parallel Weyl tensor, which are Ricci-recurrent, but neither conformally flat nor locally symmetric, and represent all indefinite…
Within the post Newtonian framework the fully reduced Hamiltonian (i.e., with eliminated spin supplementary condition) for the next-to-leading order spin-squared dynamics of general compact binaries is presented. The Hamiltonian is…
The purpose of this paper is to analyze in detail the Hamiltonian formulation for the compact Gowdy models coupled to massless scalar fields as a necessary first step towards their quantization. We will pay special attention to the coupling…