Fermionic equations of motion in strongly-correlated media: applications to the nuclear many-body problem

TL;DR

This paper provides an overview of strongly coupled quantum many-body theory with a focus on nuclear structure, emphasizing analytical methods and the unifying quantum field theory framework connecting various nuclear models.

Contribution

It offers a unified, model-independent quantum field theory approach to nuclear many-body problems, clarifying connections between different theoretical methods.

Findings

Connections between ab initio, density functional, and beyond mean-field models.

Analytical insights into excited states of medium-heavy nuclei.

Emphasis on the universal framework for nuclear dynamics.

Abstract

These notes summarise the lectures given at the International School of Physics "Enrico Fermi" in Summer 2024 in Varenna (Italy) about the strongly coupled quantum many-body theory and its applications to nuclear structure. The lectures present a rather short overview of the subject with an emphasis on the analytical aspects of the nuclear many-body problem, aiming at a deep understanding of the complexity of strongly coupled nucleonic states and emergent collective phenomena. The major pedagogical focus is recognizing how all the models describing nuclear dynamics follow from a unified model-independent framework formulated in the universal language of quantum field theory. In particular, connections between the classes of ab initio, density functional theory, and beyond mean-field approaches are made accessible. Approximations of varying complexity are discussed in applications to excited states of medium-heavy nuclei.