QUANTUM DENSITY-FLUCTUATIONS IN THE CHERN-SIMONS SYSTEM

We consider a quantized bosonic matter with the Chem-Simons gauge interaction in terms of the collective field based on the 1/N expansion. The Bogomol'nyi limit appears in the presence of a homogeneous external magnetic field. We investigate fluctuations around the corresponding constant density solution. Quantum density fluctuations have a gap in the excitation spectrum owing to the long-range statistical interaction. Two phases of the Chem-Simons system appear depending on the value of the statistical parameter.