engleski

Matrix formulation of Calogero-type models

We study a single matrix oscillator with the quadratic Hamiltonian and deformed commutation relations. It is equivalent to the multispecies Calogero model in one dimension, with inverse-square two-body and three-body interactions. Specially, a new matrix realization of the Calogero model for identical particles have been constructed, without using exchange operators. The critical points at which singular behaviour occurs are briefly discussed. At the end, a connection of a quantum matrix oscillator to a modified matrix Chern-Simons model is established. The quantum mechanics of electrons in the lowest Landau level is shown to be described by the matrix oscillator model with the ground state wave function of the Laughlin type.

matrix oscillator; Bargmann representation; Fock space

nije evidentirano