Random phase approximation and extensions applied to a bosonic field theory

An application of a self-consistent version of RPA to quantum field theory with broken symmetry is presented. Although our approach can be applied to any bosonic field theory, we specifically study the ϕ⁴ theory in 1 + 1 dimensions. We show that the standard RPA approach leads to an instability which can be removed when going to a superior version, i.e. the renormalized RPA. We present a method based on the so-called charging formula of the many-electron problem to calculate the correlation energy and the RPA effective potential. Received: 18 February 2002 / Accepted: 8 May 2002