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

✍ Scribed by A. Jevicki; B. Sakita

• Book ID: 116143255
• Publisher: Elsevier Science
• Year: 1980
• Tongue: English
• Weight: 863 KB
• Volume: 165
• Category: Article
• ISSN: 0550-3213
• DOI: 10.1016/0550-3213(80)90046-2

✦ Synopsis

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.