Integrating out the Dirac sea in the Walecka model

Abstract

We derive a purely fermionic no-sea effective theory, featuring positive-energy states only for the Walecka model. In contrast to the so-called mean-field theory approach with the no-sea approximation, where the Dirac sea is simply omitted from the outset, we turn to the relativistic Hartree approximation and explicitly construct a no-sea effective theory from the underlying quantum field theory. Several results obtained within these two approaches are confronted with each other. This sheds new light on the reliability of the mean-field theory with the no-sea approximation as well as the role of the Dirac sea. Restricting to $1+1$ dimensions, we obtain new analytical insights into nonuniform nuclear matter.