New method to calculate the<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>n</mml:mi></mml:math>-particle irreducible effective action

Carrington, M. E.; Yun, Guo

doi:10.1103/physrevd.85.076008

Cited by 10 publications

(7 citation statements)

References 47 publications

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“…We will use G for a self-consistent propagator and V for a self-consistent vertex. The result for the 4 loop 4PI effective action in the symmetric theory has the form [31,32] We now discuss the functional renormalization group method. The basis of the method is that we add to the action in (2) a non-local regulator term…”

Section: Preliminariesmentioning

confidence: 99%

“…2PI effective actions have been used for almost 20 years to study the thermodynamics of quantum fields [12][13][14][15][16], transport coefficients [17][18][19][20], and non-equilibrium quantum dynamics [21][22][23][24][25][26][27][28]. On the other hand, while higher order effective actions have been derived using several different methods [29][30][31][32], very little progress has been made in solving the resulting variational equations. We comment that although we could try to ignore vertex corrections and improve previous 2PI calculations by increasing the order of the truncation (usually the loop order), it is known that nPI formulations with n > 2 are necessary in some situations.…”

Section: Introductionmentioning

confidence: 99%

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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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Section: Preliminariesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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

et al. 2019

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“…The dashed lines represent the resummed propagators ∆. Note that these diagrams are called "eight," "egg," "mercedes," "hair," and "bball" respectively in the nomenclature of [4,5].…”

Section: Review Of Npi Effective Actionsmentioning

confidence: 99%

“…On the finite temperature and density fronts, efficient functional methods in the form of n-particle irreducible effective actions (nPIEA) have proven useful to understand collective behaviour and phase transitions [2]. They are similar in spirit to methods based on Schwinger-Dyson equations in field theory or BBGKY (Bogoliubov-Born-Green-Kirkwood-Yvon) equations in kinetic theory however, unlike the Schwinger-Dyson or BBGKY equations, nPIEA naturally form closed systems of equations of motion without requiring any closure ansatz [3][4][5]. nPIEA methods can be understood as a hybrid of variational and perturbative methods: nPIEA consist of a series of Feynman diagrams, however the propagators and vertices of these diagrams are the exact 1-through n-point * michael.brown6@my.jcu.edu.au proper connected correlation functions which are determined self-consistently using variational equations of motion.…”

Section: Introductionmentioning

confidence: 99%

Symmetry improvement of 3PI effective actions forO(N)scalar field theory

Brown

Whittingham

2015

Phys. Rev. D

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n-Particle Irreducible Effective Actions (nPIEA) are a powerful tool for extracting nonperturbative and non-equilibrium physics from quantum field theories. Unfortunately, practical truncations of nPIEA can unphysically violate symmetries. Pilaftsis and Teresi (PT) addressed this by introducing a "symmetry improvement" scheme in the context of the 2PIEA for an O (2) scalar theory, ensuring that the Goldstone boson is massless in the broken symmetry phase [A. Pilaftsis and D. Teresi, Nuclear Physics B 874, 2 (2013), pp. 594-619.]. We extend this idea by introducing a symmetry improved 3PIEA for O (N ) theories, for which the basic variables are the one-, twoand three-point correlation functions. This requires the imposition of a Ward identity involving the three-point function. We find that the method leads to an infinity of physically distinct schemes, though a field theoretic analogue of d'Alembert's principle is used to single out a unique scheme. The standard equivalence hierarchy of nPIEA no longer holds with symmetry improvement and we investigate the difference between the symmetry improved 3PIEA and 2PIEA. We present renormalized equations of motion and counter-terms for two and three loop truncations of the effective action, though we leave their numerical solution to future work. We solve the Hartree-Fock approximation and find that our method achieves a middle ground between the unimproved 2PIEA and PT methods. The phase transition predicted by our method is weakly first order and the Goldstone theorem is satisfied, while the PT method correctly predicts a second order phase transition. In contrast, the unimproved 2PIEA predicts a strong first order transition with large violations of the Goldstone theorem. We also show that, in contrast to PT, the two loop truncation of the symmetry improved 3PIEA does not predict the correct Higgs decay rate although the three loop truncation does, at least to leading order. These results suggest that symmetry improvement should not be applied to nPIEA truncated to < n loops. We also show that symmetry improvement schemes are compatible with the Coleman-Mermin-Wagner theorem, giving a check on the consistency of the formalism.

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“…There is evidence therefore that higher order nPI calculations are important and worth-while to persue. Higher order effective actions have been derived using different methods [65,[67][68][69], but little progress has been made in solving the resulting variational equations.…”

Section: Introductionmentioning

confidence: 99%

2PI effective theory at next-to-leading order using the functional renormalization group

et al. 2018

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We consider a symmetric scalar theory with quartic coupling in 4-dimensions. We show that the 4 loop 2PI calculation can be done using a renormalization group method. The calculation involves one bare coupling constant which is introduced at the level of the Lagrangian and is therefore conceptually simpler than a standard 2PI calculation, which requires multiple counterterms. We explain how our method can be used to do the corresponding calculation at the 4PI level, which can not be done using any known method by introducing counterterms. * carrington@brandonu.ca †

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New method to calculate then-particle irreducible effective action

Cited by 10 publications

References 47 publications

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

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

Symmetry improvement of 3PI effective actions forO(N)scalar field theory

2PI effective theory at next-to-leading order using the functional renormalization group

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