Liouville-Neumann Approach to the Nonperturbative Quantum Field Theory

Abstract

We present a nonperturbative field theoretic method based on the Liouville-Neumann (LN) equation. The LN approach provides a unified formulation of nonperturbative quantum fields and also nonequilibrium quantum fields, which makes use of mean-field type equations and whose results at the lowest level are identically the same as those of the Gaussian effective potential approach and the mean-field approach. The great advantageous point of this formulation is its readiness of applicability to time-dependent quantum systems and to finite temperature field theory, and its possibility to go beyond the Gaussian approximation.

To appear in the proceedings to be published by World Scientific of APCTP-ICTP Joint International Conference '97 on 'Recent Developments in Nonperturbative Quantum Field Theory', May 26-30, 1997, Seoul, Some typos corrected, ReVTeX, 12 Pages, No Figure