2D Calogero model in the collective-field approach

We consider the large-N Calogero-Marchioro model in two dimensions in the Hamiltonian collective-field approach based on the 1/N expansion. The Bogomol'nyi limit appears in the presence of the harmonic confinement. We investigate density fluctuations around the semiclassical uniform solution. The excitation spectrum splits into two branches depending on the value of the coupling constant. The ground state exhibits long-range order.