Should Unstable Quantum Field Theories be Lorentz-invariant?

An unstable field theory is what we obtain when linearise the equations of an interacting near state. Theories this kind are adopted to model onset spontaneous symmetry breakings, fields sitting on top Mexican hat, and they start ''roll down'' bottom. At present, there exists no rigorous proof that quantum theories Lorentz-invariant (in sense Wigner's theorem). Here, show shouldn't be. In fact, always have a limited regime applicability, valid only for very short time. As consequence, preferred simultaneity hyperplane, along which everywhere applicable, while generic observer (whose four-velocity not orthogonal such hyperplane) must use full non-linear theory. summary: current quantization schemes ''ok'', independently from whether lead