On the breaking and restoration of symmetries within the nuclear energy density functional formalism

TL;DR

This paper reviews symmetry breaking and restoration in nuclear energy density functional methods, highlighting differences from wave-function approaches and proposing constraints to improve symmetry restoration within the energy functional framework.

Contribution

It identifies key challenges in symmetry restoration within energy density functional methods and suggests new constraints to enhance the formalism.

Findings

Differences between wave-function and energy functional methods are clarified.

Difficulties in symmetry restoration within the energy functional framework are discussed.

Potential constraints to improve symmetry restoration are proposed.

Abstract

We review the notion of symmetry breaking and restoration within the frame of nuclear energy density functional methods. We focus on key differences between wave-function- and energy-functional-based methods. In particular, we point to difficulties encountered within the energy functional framework and discuss new potential constraints on the underlying energy density functional that could make the restoration of broken symmetries better formulated within such a formalism. We refer to Ref.~\cite{duguet10a} for details.