The Vacuum in the Label Framework: Two Sources, One Geometry, q-Theory and What Labels Leave Free

In the label framework matter is a field of comoving labels whose relabellings preserve the label volume. We collect what it says about the vacuum. A Lorentz-invariant stress is a multiple of the metric, so w=p/ρ=−1 where it is non-zero. Of media of one to four labels with an action F(n) of the label density n, only four labels give such a stress for every configuration and F. Classically, under the trace-free equation or in the four-label medium with non-degenerate gradients and F″≠0, Λ is a constant of integration: its value is initial data. The four-label medium realises the q-theory of Klinkhamer and Volovik, with q=n and vacuum energy density ε(q)=−F. Under a gauge premise on local relabellings, stated in the introduction, this classical vacuum has no local excitations. A zero Λ in q-theory needs an isolated vacuum. The value of Λ and the quantum vacuum lie beyond the framework.