The (φ 4)3 + 1 theory with infinitesimal bare coupling constants

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].…”

“…One way is to continue using the variational method with more elaborate, non-Gaussian trial wavefunctionals. For example, Kümmel and his collabrators developed the coupled cluster method and obtained results beyond the Gaussian approximation of the λφ 4 and φ 6 models [9]; Ritschel and his collaborators constructed a non-Gaussian trial wave functionals through a nonlinear canonical transformation [10]; In order to investigate (3 + 1)-dimentional λφ 4 field theory, Yotsuyanagi proposed an improved scheme of the GWFA by adopting a BCS-type wavefunctional [11]. Another way of improveing the GWFA is to use appropriate expansions which give the GEP in their lowest order.…”

Restoration and breakdown of the ϕ→-ϕ symmetry in the (1+1)-dimensional massive sine-Gordon field theory by quantum and finite-temperature effects

“…[1,15,16]. Although an investigation with the help of some better approximate methods [40] would perhaps have different numerical results about the 2D MSGFT, the results in this paper will provide a basis and a reference at least, for to our knowledge, no quantitative results about the restoration and dynamical breakdown of Z 2 -symmetry in the 2D MSGFT existed in the literature.…”

CRUCIAL DEPENDENCE OF "PRECARIOUS" AND "AUTONOMOUS" ϕ4's UPON THE NORMAL-ORDERING MASS

“…(10), there is not the denominator (1 + 3a 1 ) at all, and the appearance of this denominator is due to a mathematical deformation of rewriting Eq. (7). Additionally, although the solution (i) can make Eqs.…”

“…Additionally, although the solution (i) can make Eqs. (6) and (7) have no explicit divergences (of course except for a divergent constant in Eq. (6)), it means that λ is finite and therefore does not produce a viable theory, for the vacuum could become unstable [2].…”