Integrating out the Dirac sea in the Walecka model

TL;DR

This paper develops a fermionic no-sea effective theory for the Walecka model, explicitly deriving it from quantum field theory and comparing it with mean-field approaches to assess the Dirac sea's role.

Contribution

It introduces a new derivation of a no-sea effective theory from quantum field theory, providing analytical insights and comparison with mean-field methods.

Findings

The no-sea effective theory aligns with the relativistic Hartree approximation.

Comparison reveals limitations of the mean-field no-sea approach.

Analytical solutions for nonuniform nuclear matter in 1+1 dimensions are obtained.

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.