The quantum collective field method and its application to the planar limit

We formulate a general method of collective fields in quantum theory, which represents a direct generalization of the Bohm-Pines treatment of plasma oscillations. The present method provides a complete procedure for reformulating a given quantum system in terms of a most general (overcomplete) set of commuting operators. We point out and exemplify how this formalism offers a new powerful method for studying the large-N limit. For illustration we discuss the collective motions of N identical harmonic oscillators. As a much more important application, we show how, based on the present formalism, one solves the planar limit of a non-trivial SU(N) symmetric quantum theory. (orig.)