Road to EFT for EDFs: Variational Perturbation Theory for Effective Actions

Nuclear energy density functionals (EDFs) have been used with success to describe emergent features of nuclear systems. They suffer, however, from a lack of a systematic way to improve predictive accuracy. Casting the nuclear EDF as an effective field theory (EFT) is desirable since the hallmark features of an EFT would address precisely the current weaknesses of nuclear EDFs. There are multiple avenues of exploration for formulating such an EFT; my work is centered around formulating the EDF as an effective action, focusing first on constructing an expansion of correlations in different channels for collective variables when defining the action. The traditional path towards collective variables in a quantum field theory is the Hubbard-Stratonovich transformation (HST). While formally exact, the HST picks only one channel for a collective coordinate, meaning physics from other channels may be obscured. I will present an adaptation of Variational Perturbation Theory - a method of rewriting the path integral that allows for the inclusion of multiple auxiliary parameters in an optimizable manner- as a way of introducing collective fields for all channels when constructing the Effective Action.