Variational perturbation scheme for many-particle systems in the functional integral approach

Abstract

A variational perturbation theory based on the functional integral approach is formulated for many-particle systems. Using the variational action obtained through Jensen-Peierls' inequality, a perturbative expansion scheme for the thermodynamic potential is established. A modified Wick's theorem is obtained for the variational perturbation expansions. This theorem allows one to carry out systematic calculations of higher order terms without worrying about the double counting problem. A model numerical calculation was carried out on a nucleon gas system interacting through the Yukawa-type potential to test the efficiency of the present method.

Erratum: Rayleigh-Schrödinger perturbation theory based on Gaussian wave functional approach [Phys. Rev. D64, 025006 (2001)]

“…The Gaussian effective potential (GEP) obtained from the GWFA provides a good starting point for further investigations of various systems [9][10][11][12][13][14][15][16][17]. Moreover, this approximation can also be used for realizing some novel ideas [18].…”

“…In this aspect, Okopińska developed an optimized expansion method to calculate the generating functional with the Euclidean formalism [12] ; In the same Euclidean formalism, Stancu and Stevenson formulated a slightly different expansion scheme and calculated the post-GEP in the spirit of the background-field method [13]; Based on the GEP, Cea proposed a generalized GEP with a variational basis and carried out the calculation with the help of the standard perturbation technique in quantum field theory [14]; In the late 1990s, within the Minkowski formalism, one of the authors (Yee) and his collabrators developed the background field method to give an expansion of the effective action around the Gaussian approximate results [15]. Recently, in order to calculate the partition function of a fermionic system, two of the authors (Kim and Nahm) and their collaborator proposed a variational perturbation scheme based on the functional integral without resorting to the background field method [16]. Additionally, Solovtsov et al proposed a kind of variational perturbation theory to calculate the effective potential [17].…”

Rayleigh-Schr�dinger-Goldstone variational perturbation theory for many Fermion systems

“…We find that the above ground state energy is same as the zero temperature limit of the variational perturbation theory [25] previously obtained from a functional integral representation, because Gaussian approximations of both representations employed same variational basis. For a numerial energy value, we modeled an electron gas with a bare kinetic energy ǫ…”

“…It was shown that this approach gives successful results on Gaussian approximations of fermi fields as in bose fields. However, in contrast to the bosonic case [1], no successful Rayleigh-Schrödinger type perturbation formalism for fermi fields has been proposed so far, although several alternative schemes including functional integrals [25] and background field methods [8] have been reported using the FloreaniniJackiw representation(FJR). Since the Rayleigh-Schrödinger perturbation formalism is the most familiar form of perturbation theories and especially suitable for the Schödinger picture representation in quantum mechanics, it is rather puzzling that it is not so in field theories.…”

Variational perturbation approach to the Coulomb electron gas

“…Recently, papers on another kind of VPT have been published [15][16][17][18]. This approach is not related to the PMS, because the minimization is carried out at the zeroth order and the variational parameters are fixed before the perturbative calculation.…”