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

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