Progress towards EFT for EDFs: Symmetry restoration techniques with Effective Actions

Nuclear energy density functionals (EDFs) have been used with success to describe emergent features of nuclear systems. Casting the nuclear EDF as an effective field theory (EFT) will enable improved uncertainty quantification, power counting for improvements to functionals, and identification of the limits of the functional's predictions. There are many ongoing challenges in the effort to formulate EDFs as an EFT, some inherent to specific avenues towards doing so. We are applying the background field formalism, casting the EDF as an effective action. In reference [1], we showed how to apply Variational Perturbation Theory to the calculation of the effective action as a way of incorporating beyond mean field physics in multiple channels for a uniform system. Another challenge that becomes pertinent for finite systems is to restore broken symmetries at the mean field level and beyond. Here, we present an approach based on the BRST quantization scheme, which has been widely used in gauge theories as a way of enforcing that calculations of observables obey constraints.

[1] arxiv:2506.02919