Relativity of non relativistic systems

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To the best of our knowledge, the fundamental laws of physics are Lorentz invariant. This means that condensed matter systems at finite density still display full Lorentz symmetry: it is just spontaneously broken (i.e. by state considered) and thus non-linearly realized. This simple observation allows to derive exact results about the spectrum of theories at finite charge density and suggests to classify condensed matter systems according to all the inequivalent ways in which boosts can be spontaneously broken.