Linear response theory for symmetry improved two particle irreducible effective actions

Brown, Michael J.; Whittingham, Ian B.; Kosov, Daniel S.

doi:10.1103/physrevd.93.105018

Cited by 5 publications

(10 citation statements)

References 27 publications

(38 reference statements)

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“…Solutions are then found in section IV with careful consideration of the various Vβ → ∞ limits. Finally, we discuss our results in section V. The notation agrees with our previous papers [22,23] except where noted. In particular, the deWitt summation convention is used, i.e.…”

Section: Introductionsupporting

confidence: 71%

“…The soft symmetry improved 2PIEA is a modification of the 2PIEA defined for theories with an internal symmetry. In order to have a concrete example we use the O (N ) symmetric scalar φ 2 2 theory discussed in our previous papers [22,23]. We will focus on the spontaneous symmetry breaking regime where the field has a non-zero expectation value ϕ a = φ a = (0, .…”

Section: Soft Symmetry Improvement Of 2pieamentioning

confidence: 99%

“…The constraint is singular, meaning one must proceed by violating the constraint by an amount ∼ η then taking a limit η → 0 such that η is a constant. In the previous literature [14,22,23] this procedure was carried out at the level of the equations of motion. Now it is convenient to implement this at the level of the action by shifting the constraint term to…”

Section: B Symmetric Phasementioning

confidence: 99%

“…Pilaftsis and Teresi [14] introduced a promising method called symmetry improvement (SI), which imposes the WIs directly as constraints on the solution through Lagrange multipliers. SI has been applied with some success with the SI-2PIEA [14,[18][19][20][21] and extended to the SI-3PIEA [22], however the method is inconsistent out of equilibrium (at least at the linear response level) [23] and sometimes solutions fail to exist due to the constraint causing a renormalization group defying coupling between short and long distance physics [24]. Considering that the symptom in both cases is the non-existence of solutions, and that the constraint in the SI method is singular and requires some careful treatment to begin with, it is reasonable to suspect that the culprit may be that the method is over-constraining.…”

Section: Introductionmentioning

confidence: 99%

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Soft symmetry improvement of two particle irreducible effective actions

Brown

Whittingham

2017

Phys. Rev. D

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Two particle irreducible effective actions (2PIEAs) are valuable non-perturbative techniques in quantum field theory; however, finite truncations of them violate the Ward identities (WIs) of theories with spontaneously broken symmetries. The symmetry improvement (SI) method of Pilaftsis and Teresi attempts to overcome this by imposing the WIs as constraints on the solution; however the method suffers from the non-existence of solutions in linear response theory and in certain truncations in equilibrium. Motivated by this, we introduce a new method called soft symmetry improvement (SSI) which relaxes the constraint. Violations of WIs are allowed but punished in a least-squares implementation of the symmetry improvement idea. A new parameter $\xi$ controls the strength of the constraint. The method interpolates between the unimproved ($\xi \to \infty$) and SI ($\xi \to 0$) cases and the hope is that practically useful solutions can be found for finite $\xi$. We study the SSI-2PIEA for a scalar O(N) model in the Hartree-Fock approximation. We find that the method is IR sensitive: the system must be formulated in finite volume $V$ and temperature $T=\beta^{-1}$ and the $V\beta \to \infty$ limit taken carefully. Three distinct limits exist. Two are equivalent to the unimproved 2PIEA and SI-2PIEA respectively, and the third is a new limit where the WI is satisfied but the phase transition is strongly first order and solutions can fail to exist depending on $\xi$. Further, these limits are disconnected from each other; there is no smooth way to interpolate from one to another. These results suggest that any potential advantages of SSI methods, and indeed any application of (S)SI methods out of equilibrium, must occur in finite volume.Comment: Two ancillary Mathematica notebooks included: one for renormalization and one for solving the finite equations of motion. Uses pdflatex. 18 pages, 9 figures. Submitted to PRD. v2 changes: a number of stylistic improvements and a few references adde

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Section: Introductionsupporting

confidence: 71%

Section: Soft Symmetry Improvement Of 2pieamentioning

confidence: 99%

Section: B Symmetric Phasementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Soft symmetry improvement of two particle irreducible effective actions

Brown

Whittingham

2017

Phys. Rev. D

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“…A major disadvantage of nPI methods is a violation of gauge invariance [6,7]. A procedure to minimize gauge dependence has been proposed [8], and some issues with applying the tehcnique are discussed in [9][10][11].…”

Section: Introductionmentioning

confidence: 99%

Renormalization of the 4PI effective action using the functional renormalization group

et al. 2019

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Techniques based on n-particle irreducible effective actions can be used to study systems where perturbation theory does not apply. The main advantage, relative to other non-perturbative continuum methods, is that the hierarchy of integral equations that must be solved truncates at the level of the action, and no additional approximations are needed. The main problem with the method is renormalization, which until now could only be done at the lowest (n=2) level. In this paper we show how to obtain renormalized results from an n-particle irreducible effective action at any order. We consider a symmetric scalar theory with quartic coupling in four dimensions and show that the 4 loop 4-particle-irreducible calculation can be renormalized using a renormalization group method. The calculation involves one bare mass and one bare coupling constant which are introduced at the level of the Lagrangian, and cannot be done using any known method by introducing counterterms. * carrington@brandonu.ca †

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Loss of solution in the symmetry improved Φ-derivable expansion scheme

2016

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International audienceWe consider the two-loop Φ-derivable approximation for the O(2) -symmetric scalar model, augmented by the symmetry improvement introduced in Pilaftsis and Teresi (2013) [9] , which enforces Goldstone's theorem in the broken phase. Although the corresponding equations admit a solution in the presence of a large enough infrared (IR) regulating scale, we argue that, for smooth ultraviolet (UV) regulators, the solution is lost when the IR scale becomes small enough. Infrared regular solutions exist for certain non-analytic UV regulators, but we argue that these solutions are artifacts which should disappear when the sensitivity to the UV regulator is removed by a renormalization procedure. The loss of solution is observed both at zero and at finite temperature, although it is simpler to identify in the latter case. We also comment on possible ways to cure this problem

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Linear response theory for symmetry improved two particle irreducible effective actions

Cited by 5 publications

References 27 publications

Soft symmetry improvement of two particle irreducible effective actions

Soft symmetry improvement of two particle irreducible effective actions

Renormalization of the 4PI effective action using the functional renormalization group

Loss of solution in the symmetry improved Φ-derivable expansion scheme

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