1/N expansion, vacuum stability and quark confinement

Abstract

A method is suggested which makes possible the investigation of the ultraviolet (infrared) behaviour of a class of ultraviolet (infrared) unstable theories. By the use of this method we argue that the theory λϕ4/N of the N-component field ϕ at all sufficiently large N and for any sign of λ is unstable with respect to the spontaneous generation of an infinitely large classical field ϕ. It is also pointed out that in the infrared unstable massless theory λϕ4N at λ < 0 the effective coupling constant is not singular at vanishing momenta. This means that the infrared instability does not necessarily imply "infrared slavery".