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Hadrons and Nuclei


Eur. Phys. J. A 14, 397-411 (2002)
DOI: 10.1140/epja/i2002-10023-y

Random phase approximation and extensions applied to a bosonic field theory

H. Hansen1, G. Chanfray1, D. Davesne1 and P. Schuck2

1  IPN Lyon, 43 Bd du 11 Novembre 1918, F-69622 Villeurbanne Cedex, France
2  IPN Orsay, Université Paris-Sud, France

hansen@ipnl.in2p3.fr

(Received: 18 February 2002 Communicated by V. Vento)

Abstract
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 $\varphi^4$ 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.

PACS
03.70.+k - Theory of quantized fields.
21.60.Jz - Hartree-Fock and random-phase approximations.
24.10.Cn - Many-body theory.

© Società Italiana di Fisica, Springer-Verlag 2002