On the Ground State of O(N)- 4 Model

Abstract

A possible ground state of O(N)-λφ4 model is found in the leading order of 1/N expansion. This vacuum does not break the O(N) symmetry and all components of φ have a common mass. The renormalized coupling constant on this vacuum is always found to be negative irrespective of the initial coupling renormalized at some point. The four-point Green's function has no tachyon poles on this ground state contrary to the situations on the old one. Plausible arguments for these features to remain also in higher orders are given. Many similarities are noted with the theory with a negative bare coupling constant in 2 (or 1 or 3) dimensions. Stability of the theory is also discussed.