Renormalizing the Schwinger-Dyson equations in the auxiliary field formulation of<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>λ</mml:mi><mml:msup><mml:mi>ϕ</mml:mi><mml:mn>4</mml:mn></mml:msup></mml:math>field theory

Cooper, Fred; Mihaila, Bogdan; Dawson, John F.

doi:10.1103/physrevd.70.105008

Cited by 39 publications

(61 citation statements)

References 63 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…It has been shown, in particular, that the resummation equation for the two-point function in the context of scalar ϕ 4 -theories can be made finite by adjusting a finite number of local counterterms. A similar analysis [20] has recently been performed for the 2PI 1/N-expansion [8,21]. Although this allows one to compute various physical quantities such as the thermodynamic pressure, we emphasize that the renormalization presented in these works is not sufficient to fix all counterterms needed to compute the proper vertices encoded in Γ [φ].…”

Section: Introductionmentioning

confidence: 91%

Nonperturbative renormalization for 2PI effective action techniques

et al. 2005

View full text Add to dashboard Cite

Nonperturbative approximation schemes based on two-particle irreducible (2PI) effective actions provide an important means for our current understanding of (non-)equilibrium quantum field theory. A remarkable property is their renormalizability, since these approximations involve selective summations to infinite perturbative orders. In this paper we show how to renormalize all n-point functions of the theory, which are given by derivatives of the 2PI-resummed effective action Γ[φ] for scalar fields φ. This provides a complete description in terms of the generating functional for renormalized proper vertices, which extends previous prescriptions in the literature on the renormalization for 2PI effective actions. The importance of the 2PI-resummed generating functional for proper vertices stems from the fact that the latter respect all symmetry properties of the theory and, in particular, Goldstone's theorem in the phase with spontaneous symmetry breaking. This is important in view of the application of these techniques to gauge theories, where Ward identities play a crucial role. *

show abstract

Section: Introductionmentioning

confidence: 91%

Nonperturbative renormalization for 2PI effective action techniques

et al. 2005

View full text Add to dashboard Cite

show abstract

“…First of all this concerns the interrelation of functional methods like the general flows studied here, Dyson-Schwinger equations [149][150][151][152][153][154][155][156][157], stochastic quantisation [158][159][160], and the use of N PI effective actions [161][162][163][164][165][166][167][168][169][170][171][172][173][174][175][176][177]. All these methods have met impressive success in the last decade, in particular if it comes to physics where a perturbative treatment inherently fails.…”

Section: Applications To Functional Methodsmentioning

confidence: 99%

“…In particular, the construction of practical consistent renormalisation schemes within truncations poses a challenge, see e.g. [164][165][166][167][168][169][170][171][172]. Such a renormalisation has to respect the symmetry and symmetry breaking pattern of the theory under investigation.…”

Section: B Composite Operators and N Pi Flowsmentioning

confidence: 99%

Aspects of the functional renormalisation group

2007

View full text Add to dashboard Cite

We discuss structural aspects of the functional renormalisation group. Flows for a general class of correlation functions are derived, and it is shown how symmetry relations of the underlying theory are lifted to the regularised theory. A simple equation for the flow of these relations is provided. The setting includes general flows in the presence of composite operators and their relation to standard flows, an important example being N PI quantities. We discuss optimisation and derive a functional optimisation criterion.Applications deal with the interrelation between functional flows and the quantum equations of motion, general Dyson-Schwinger equations. We discuss the combined use of these functional equations as well as outlining the construction of practical renormalisation schemes, also valid in the presence of composite operators. Furthermore, the formalism is used to derive various representations of modified symmetry relations in gauge theories, as well as to discuss gauge-invariant flows. We close with the construction and analysis of truncation schemes in view of practical optimisation.

show abstract

“…This is a long-standing problem [23,24] and recently a systematic method has been developed [25][26][27][28][29] to remove divergences in the -derivable approximations based on applying a Bogoliubov-Parasiuk-Hepp-Zimmerman subtraction procedure to diagrams with resummed propagators.…”

Section: Introductionmentioning

confidence: 99%

Renormalized and renormalization-group invariant Hartree-Fock approximation

Destri

Sartirana

2005

Phys. Rev. D

View full text Add to dashboard Cite

We study the renormalization problem for the Hartree-Fock approximation of the ON invariant 4 model in the symmetric phase and show how to systematically improve the corresponding diagrammatic resummation to achieve the correct renormalization properties of the effective field equations, including renormalization-group invariance with the one-loop beta function. These new Hartree-Fock dynamics is still of a mean-field type but includes memory effects which are generically nonlocal also in space.

show abstract

Renormalizing the Schwinger-Dyson equations in the auxiliary field formulation ofλϕ4field theory

Cited by 39 publications

References 63 publications

Nonperturbative renormalization for 2PI effective action techniques

Nonperturbative renormalization for 2PI effective action techniques

Aspects of the functional renormalisation group

Renormalized and renormalization-group invariant Hartree-Fock approximation

Contact Info

Product

Resources

About