QUANTUM-THEORY OF THE 2-DIMENSIONAL INTERACTING-BOSON SYSTEM

In this paper we expand the microscopic Hamiltonian of a self-interact ing boson system in terms of the density and phase operators, which ar e canonical conjugates to each other. When higher-order terms are negl ected, the Hamiltonian can be diagonalized. This method is applied to superfluid helium and the fractional quantum Hall effect. We shall fir st derived the expression of superfluid density for two-dimensional (2 D) system where canonical treatment haas been lacking. We then reprodu ce the 3D results obtained by the bogoliubov transformation. Finally, we shall show that the basic phenomenologies of the fractional quantum Hall effect at exact filling numbers can be derived without the intro duction of the chern-simons term.