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 SU(ν) spins, a hidden symmetry is the SU(ν)U(1)U(ν) current algebra. The system has a higher symmetry, the W1+ algebra. This W algebra structure unifies the Calogero type (1x2 interactions) and the Sutherland type (1sin2x interactions). The energy spectra of the systems are obtained in a simple manner based on the fermion representation of the algebra.
All Science Journal Classification (ASJC) codes
- Physics and Astronomy(all)