On the formalism of relativistic many body theory

Norton, Richard; Cornwall, John M.

doi:10.1016/0003-4916(75)90281-x

Cited by 112 publications

(80 citation statements)

References 13 publications

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“…This form of the effective action can be rewritten as a diagrammatic series in terms of skeleton diagrams of the n-point vertex functions [12] and can be used for generalized Φ-derivable approximations.…”

Section: Pi Effective Action and φ-Derivable Approximationsmentioning

confidence: 99%

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Gauge-fixing dependence ofΦ-derivable approximations

2002

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Abstract. We examine the problem of gauge dependence of the 2PI effective action and its Φ-derivable approximations in gauge theories. The dependence on the gauge-fixing condition is obtained. The result shows that Φ-derivable approximations, defined as truncations of the 2PI effective action at a certain order, have a controlled gauge dependence, i.e. the gauge dependent terms appear at higher order than the truncation order. Furthermore, using the stationary point obtained for the approximation to evaluate the complete 2PI effective action boosts the order at which the gauge dependent terms appear to twice the order of truncation. We also comment on the significance of this controlled gauge dependence.

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Section: Pi Effective Action and φ-Derivable Approximationsmentioning

confidence: 99%

“…Indeed, one can explicitly compute their gauge dependence by applying the condition (12) to Eqs. (28) and (29), obtaining in this manner…”

Section: Gauge-fixing Dependence Of the 2pi Effective Actionmentioning

confidence: 99%

Gauge-fixing dependence ofΦ-derivable approximations

2002

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“…At any given order of this loopwise expansion, the 2PI effective action contains an infinite set of diagrams induced by partially resummed propagators. There is an extensive literature related to the CJT formalism, within the context of thermal field theory [4,5], with the aim to address various problems of equilibrium and non-equilibrium dynamics (e.g. see [6] and references therein).…”

Section: Introductionmentioning

confidence: 99%

Symmetry-improved CJT effective action

2013

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The formalism introduced by Cornwall, Jackiw and Tomboulis (CJT) provides a systematic approach to consistently resumming non-perturbative effects in Quantum Thermal Field Theory. One major limitation of the CJT effective action is that its loopwise expansion introduces residual violations of possible global symmetries, thus giving rise to massive Goldstone bosons in the spontaneously broken phase of the theory. In this paper we develop a novel symmetry-improved CJT formalism for consistently encoding global symmetries in a loopwise expansion. In our formalism, the extremal solutions of the fields and propagators to a loopwise truncated CJT effective action are subject to additional constraints given by the Ward identities due to global symmetries. By considering a simple O(2) scalar model, we show that, unlike other methods, our approach satisfies a number of important field-theoretic properties. In particular, we find that the Goldstone boson resulting from spontaneous symmetry breaking of O (2) is massless and the phase transition is a second order one, already in the Hartree-Fock approximation. After taking the sunset diagrams into account, we show how our approach properly describes the threshold properties of the massless Goldstone boson and the Higgs particle in the loops. Finally, assuming minimal modifications to the Hartree-Fock approximated CJT effective action, we calculate the corresponding symmetryimproved CJT effective potential and discuss the conditions for its uniqueness for scalar-field values away from its minimum.

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“…The nPI effective action formalism [1][2][3][4][5][6][7] is a non-perturbative approach in which the action is expressed as a functional of n-point functions which are determined through self-consistent stationary equations after the effective action is expanded to some order in the loop or 1/N expansion. These self-consistent equations of motion resum certain classes of diagrams to infinite order.…”

Section: Introductionmentioning

confidence: 99%

Techniques for calculations withnPI effective actions

M.E.

2015

EPJ Web of Conferences

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Abstract. We consider a symmetric scalar theory with quartic coupling in 2-and 3-dimensions and compare the self-consistent 4-point vertex obtained from the 4PI effective action with the Bethe-Salpeter 4-vertex from 2PI effective action. We show that when the coupling is large the contributions from the higher order effective action are large. We also show that one can solve the 2PI equations of motion in 4-dimensions, without introducing counter-terms, using a renormalization group method. This method provides a promising starting point to study the renormalization of higher order nPI theories.

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On the formalism of relativistic many body theory

Cited by 112 publications

References 13 publications

Gauge-fixing dependence ofΦ-derivable approximations

Gauge-fixing dependence ofΦ-derivable approximations

Symmetry-improved CJT effective action

Techniques for calculations withnPI effective actions

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