Algebraic approach to quantum many-body systems of Calogero-Sutherland type

A. Latifi, H. Rahmati

Nakka Gurappa, Priti S. Mohanty, Prasanta Kumar Panigrahi

A realization is provided for the scattering states of the N-particle Calogero-Moser Hamiltonian. They are explicitly shown to be the coherent states of the singular oscillators of the Calogero-Sutherland model. Our algebraic treatment is straightforwardly extendable to a large number of few- and many-body interacting systems in one and higher dimensions.

Marcia Tenser, Amilcar R. Queiroz

We study Yang-Mills theory coupled to a particle on a cylinder, where gauge invariance and compactness reduce the dynamics to a finite dimensional quantum system. In the Abelian case, this yields a model equivalent to the Landau problem on a torus, with a degenerate ground state structure. We generalize this construction to non-Abelian gauge groups and show that, for SU(N), the system reduces to a one dimensional quantum many body problem with a singular Calogero-Sutherland-type interaction.

靖 小森

Kazuhiro Hikami, Miki Wadati

Quantum integrable particle systems with inverse square interactions in one-dimensional space are investigated by use of the quantum inverse scattering method. For the case of particles with $\mathrm{SU}(\ensuremath{\nu})$ spins, a hidden symmetry is the $\mathrm{SU}(\ensuremath{\nu})\ensuremath{\bigotimes}\mathrm{U}(1)\ensuremath{\simeq}\mathrm{U}(\ensuremath{\nu})$ current algebra. The system has a higher symmetry, the ${W}_{1+\ensuremath{\infty}}$ algebra. This $W$ algebra structure unifies the Calogero type ($\frac{1}{{x}^{2}}$ interactions) and the Sutherland type ($\frac{1}{{sin}^{2}x}$ interactions). The energy spectra of the systems are obtained in a simple manner based on the fermion representation of the algebra.

Vasilios Alexiades, George Siopsis