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Addressing energy density functionals in the language of path-integrals I: Comparative study of diagrammatic techniques applied to the (0+0)-D $O(N)$-symmetric $\varphi^{4}$-theory
Nuclear Theory · Submitted 27 Aug 2022
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim With these methods, we notably address the spontaneous breakdown of the $O(N)$ symmetry with care especially since spontaneous symmetry breakings (SSBs) play a paramount role in current implementations of the EDF approach.
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The abstract, sentence by sentence
The energy density functional (EDF) method is currently the only microscopic theoretical approach able to tackle the entire nuclear chart. Nevertheless, it suffers from limitations resulting from its empirical character and deteriorating its reliability. This paper is part of a larger program that aims at formulating the EDF approach as an effective field theory (EFT) in order to overcome these limitations. A relevant framework to achieve this is the path-integral (PI) formulation of quantum field theory (QFT). The latter indeed provides a wide variety of treatments of the many-body problem well suited to deal with non-perturbative interactions and to exploit a Lagrangian resulting from an EFT as a starting point. While developing the formalism in a general setting, we present a comparative study of such techniques applied to a toy model, i.e. the (0+0)-D $O(N)$-symmetric $\varphi^{4}$-theory. More specifically, our focus will be on the following diagrammatic techniques: loop expansion (LE), optimized perturbation theory (OPT) and self-consistent perturbation theory (SCPT). With these methods, we notably address the spontaneous breakdown of the $O(N)$ symmetry with care especially since spontaneous symmetry breakings (SSBs) play a paramount role in current implementations of the EDF approach.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | The energy density functional (EDF) method is currently the only microscopic theoretical approach able to tackle the entire nuclear chart. | background 1.00 | 0.05 | 0.02 | asserted 1.00 |
| s1 | Nevertheless, it suffers from limitations resulting from its empirical character and deteriorating its reliability. | background 0.87 | 0.07 | 0.02 | asserted 1.00 |
| s2 | This paper is part of a larger program that aims at formulating the EDF approach as an effective field theory (EFT) in order to overcome these limitations. | contribution 0.56 | 0.22 | 0.04 | asserted 0.97 |
| s3 | A relevant framework to achieve this is the path-integral (PI) formulation of quantum field theory (QFT). | method 0.58 | 0.07 | 0.03 | asserted 0.94 |
| s4 | The latter indeed provides a wide variety of treatments of the many-body problem well suited to deal with non-perturbative interactions and to exploit a Lagrangian resulting from an EFT as a starting point. | background 0.82 | 0.06 | 0.03 | asserted 0.99 |
| s5 | While developing the formalism in a general setting, we present a comparative study of such techniques applied to a toy model, i.e. the (0+0)-D $O(N)$-symmetric $\varphi^{4}$-theory. | contribution 0.77 | 0.88 | 0.05 | asserted 0.99 |
| s6 | More specifically, our focus will be on the following diagrammatic techniques: loop expansion (LE), optimized perturbation theory (OPT) and self-consistent perturbation theory (SCPT). | method 0.69 | 0.70 | 0.03 | asserted 0.98 |
| s7 | With these methods, we notably address the spontaneous breakdown of the $O(N)$ symmetry with care especially since spontaneous symmetry breakings (SSBs) play a paramount role in current implementations of the EDF approach. | contribution 0.93 | 0.85 | 0.09 | asserted 0.99 |
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The paper
Original abstract
The energy density functional (EDF) method is currently the only microscopic theoretical approach able to tackle the entire nuclear chart. Nevertheless, it suffers from limitations resulting from its empirical character and deteriorating its reliability. This paper is part of a larger program that aims at formulating the EDF approach as an effective field theory (EFT) in order to overcome these limitations. A relevant framework to achieve this is the path-integral (PI) formulation of quantum field theory (QFT). The latter indeed provides a wide variety of treatments of the many-body problem well suited to deal with non-perturbative interactions and to exploit a Lagrangian resulting from an EFT as a starting point. While developing the formalism in a general setting, we present a comparative study of such techniques applied to a toy model, i.e. the (0+0)-D $O(N)$-symmetric $\varphi^{4}$-theory. More specifically, our focus will be on the following diagrammatic techniques: loop expansion (LE), optimized perturbation theory (OPT) and self-consistent perturbation theory (SCPT). With these methods, we notably address the spontaneous breakdown of the $O(N)$ symmetry with care especially since spontaneous symmetry breakings (SSBs) play a paramount role in current implementations of the EDF approach.
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How the literature uses it
2 arXiv papers cite this in 2 sentences
Papers citing it
Cites it as background 2 papers
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Subsequently, Refs. [ref] use Bayesian statistics to calculate the magnitudes of truncation errors in the different EFTs.
Bayesian method for fitting the low-energy constants in chiral perturbation theory · Introduction · 0.80
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While different ideas to formulate an effective field theory (EFT) for EDFs have been discussed [ref] , none of them has been implemented yet.
Optimized nuclear energy density functionals including long-range pion contributions · Introduction · 0.97
What it cites · 18 sentences without a confident label
Cites as background 5 papers
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The 2PI EA framework[See Ref. [ref] for a pedagogical introduction on the 2PI EA.] is a direct reformulation of the Green's function formalism based on Dyson equation and the Luttinger-Ward functional [ref] .
Introduction to Nonequilibrium Quantum Field Theory · Generating functionals of interest in the path-integral formalism · 0.85
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OPT has been widely used for decades via the above optimization criteria [ref] .
Converting Divergent Weak-Coupling into Exponentially Fast Convergent Strong-Coupling Expansions · Optimized perturbation theory · 0.81
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OPT has been widely used for decades via the above optimization criteria [ref] .
Hubbard-Stratonovich Transformation: Successes, Failure, and Cure · Optimized perturbation theory · 0.81
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