Ebook: 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.