Explicit algebraic relations between the quantum integrals of the elliptic Calogero–Moser quantum problems related to the root systems A2 and B2 are found.

Two Lie algebraic forms of the 2-body Elliptic Calogero model are presented. Translation-invariant and dilatation-invariant discretizations of the model are obtained.

We apply a method of perturbation for the BC1 Inozemtsev model from the trigonometric model and show the holomorphy of perturbation. Consequently, the convergence of eigenvalues and eigenfuncions which are expressed as formal power series is proved. We investigate also the relationship between L space and some finite dimensional space of elliptic functions.

We develop a discrete analogue of the Hamilton–Jacobi theory in the framework of the discrete Hamiltonian mechanics. We first reinterpret the discrete Hamilton–Jacobi equation derived by Elnatanov and Schiff in the language of discrete mechanics. The resulting discrete Hamilton– Jacobi equation is discrete only in time, and is shown to recover the Hamilton–Jacobi equation in the continuous-time...

We construct a κ-symmetric Green-Schwarz action for type IIA string theory on AdS2. As a candidate holographic dual, we consider superconformal matrix quantum mechanics, given by the Marinari-Parisi model with vanishing or logarithmic superpotential. We derive that the super-eigenvalues form a consistent subsector, and that their dynamics reduces to that of the supersymmetric Calogero-Moser mod...

In a previous paper (Corrigan-Sasaki), many remarkable properties of classical Calogero and Sutherland systems at equilibrium are reported. For example, the minimum energies, frequencies of small oscillations and the eigenvalues of Lax pair matrices at equilibrium are all “integer valued”. The equilibrium positions of Calogero and Sutherland systems for the classical root systems (Ar, Br, Cr an...

We discuss the implications of the Calogero hypothesis on the \cosmic origin of quantization" 1], and of the variation of h with time it implies, for cosmology. We focus on two issues: (a) how the relation between redshift and distance would be modiied; and (b) how the observations on the cosmic background radiation, and the estimation they give of the time elapsed since its production, would b...

The Schrödinger operators with exchange terms for certain Calogero-Sutherland quantum many body systems have eigenfunctions which factor into the symmetric ground state and a multivariable polynomial. The polynomial can be chosen to have a prescribed symmetry (i.e. be symmetric or antisymmetric) with respect to the interchange of some specified variables. For four particular Calogero-Sutherland...

Ioannis Iraklis Haranas Physics and Astronomy Department York University 314 A Petrie Science Building Toronto – Ontario CANADA E mail: [email protected] Abstract: In a study by F. Calogero [1] entitled “ Cosmic origin of quantization” an expression was derived for the variability of h with time, and its consequences if any, of such an idea in cosmology were examined. In this paper we will offer...

To any finite group Γ ⊂ Sp(V ) of automorphisms of a symplectic vector space V we associate a new multi-parameter deformation, Hκ, of the algebra C[V ]#Γ, smash product of Γ with the polynomial algebra on V . The parameter κ runs over points of CP , where r =number of conjugacy classes of symplectic reflections in Γ. The algebra Hκ, called a symplectic reflection algebra, is expected to be rela...