On the role of the Vacuum Energy in the Thermodynamics of Neutron Matter

TL;DR

This paper investigates how vacuum energy influences the thermodynamics of neutron matter under magnetic fields, providing a method to calculate its contribution despite non-renormalisability issues, and confirming its small impact.

Contribution

It presents a way to unambiguously compute vacuum energy contributions in neutron matter with magnetic fields, addressing non-renormalisability challenges.

Findings

Vacuum energy contribution is small, supporting the no-sea approximation.

Derived explicit expression for vacuum energy in a constant magnetic field.

Discussed how density and temperature affect the grand canonical potential.

Abstract

The only way neutron matter can couple to the electromagnetic field is through an anomalous coupling, which plays an important role in the thermodynamics of pure neutron matter. Such theories are, however, perturbatively non-renormalisable, which presents a difficulty in terms of the unambiguous treatment of the divergencies. Here we show that despite this, an unambiguous expression can be obtained for the vacuum energy contribution to the grand canonical potential in the case of a constant magnetic field. We find that this contribution is quite small, which justifies the no-sea approximation usually made. We also discuss the density and temperature dependence of the full grand canonical potential.