The energy-momentum spectrum in local field theories with broken Lorentz- symmetry
Let A be a \(C^*\)-algebra of local observables, and let the translation group \({\mathbb{R}}^ d\) act on it, and look at a covariant representation with U(a) the corresponding representation of the translation group. Assuming that the spectrum of U(a) is in the forward lightcone, then, as a consequence of the locality, there exist a unique minimal representation \(U^ 0(a)\) fulfilling again the spectrum condition, and the lower boundary of its spectrum is a Lorentz invariant set.
scientific article; zbMATH DE number 3925599