Zoology of condensed matter: Framids, ordinary stuff, extra-ordinary stuff
Alberto Nicolis, Riccardo Penco, Federico Piazza, Riccardo Rattazzi

TL;DR
This paper classifies condensed matter systems based on their spacetime symmetry breaking patterns, introduces the concept of framids and galileids, and discusses their distinct physical properties and scattering behaviors.
Contribution
It provides a novel classification framework for condensed matter states using spacetime symmetries and explores new theoretical systems like framids and galileids.
Findings
Framids do not seem to be realized in Nature.
Different symmetry breaking patterns lead to distinct observable properties.
Scattering amplitudes scale differently for framids, solids, and galileids.
Abstract
We classify condensed matter systems in terms of the spacetime symmetries they spontaneously break. In particular, we characterize condensed matter itself as any state in a Poincar\'e-invariant theory that spontaneously breaks Lorentz boosts while preserving at large distances some form of spatial translations, time-translations, and possibly spatial rotations. Surprisingly, the simplest, most minimal system achieving this symmetry breaking pattern---the "framid"---does not seem to be realized in Nature. Instead, Nature usually adopts a more cumbersome strategy: that of introducing internal translational symmetries---and possibly rotational ones---and of spontaneously breaking them along with their space-time counterparts, while preserving unbroken diagonal subgroups. This symmetry breaking pattern describes the infrared dynamics of ordinary solids, fluids, superfluids, and---if they…
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