Road to EFT for nuclear EDFs

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 many avenues of exploration for formulating such an EFT; my work is centered around formulating the EDF using the background field formalism, 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). The HST faces a double counting problem when multiple channels of collective excitations are probed simultaneously. I examine and parametrize this issue here. I also present two alternative methods for examining collective modes from an EFT. The first, Kohn-Luttinger-Ward inversion, is a perturbative legendre transformation in multiple sources: one source for each channel. The second, Variational Perturbation Theory, introduces classical auxiliary fields in multiple channels exactly: without double counting.