https://doi.org/10.1140/epja/s10050-023-00933-9
Regular Article –Theoretical Physics
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 
-theory
1
CEA, DAM, DIF, 91297, Arpajon, France
2
Université Paris-Saclay, CEA, Laboratoire Matière en Conditions Extrêmes, 91680, Bruyères-le-Châtel, France
3
Institut für Theoretische Physik and Center for Quantum Science, Universität Tübingen, Auf der Morgenstelle 14, 72076, Tübingen, Germany
Received:
10
November
2022
Accepted:
26
January
2023
Published online:
28
April
2023
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 formulation of quantum field theory. 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 below a comparative study of such techniques applied to a toy model, i.e. the (0 + 0)-D O(N)-symmetric -theory. More specifically, our focus will be on the following diagrammatic techniques: loop expansion, optimized perturbation theory and self-consistent perturbation theory. With these methods, we notably address the spontaneous breakdown of the O(N) symmetry with care especially since spontaneous symmetry breakings play a paramount role in current implementations of the EDF approach.
The original online version of this article was revised:A supersource J was erroneously replaced by J in the first line of relation (143).
An erratum to this article is available online at https://doi.org/10.1140/epja/s10050-024-01297-4.
Copyright comment corrected publication 2024
Copyright comment corrected publication 2024
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© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2023. corrected publication 2024. corrected publication 2024. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
