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Random Phase Approximation and Extensions Applied to a Bosonic Field Theory

H. Hansen·G. Chanfray·D. Davesne·P. Schuck
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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 $ϕ^4$ theory in 1+1 dimensions. We show that 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.

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H. Hansen, G. Chanfray, D. Davesne, P. Schuck. 2002-09-19. Random Phase Approximation and Extensions Applied to a Bosonic Field Theory. https://arxiv.org/abs/hep-ph/0201279

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