2015/01/15 by Alberto Nicolis, Riccardo Penco, Nicolis, Alberto +5 · 8 citations
Mathematics · Physics and Astronomy · #Astro and Planetary Science #Cosmology and Gravitation Theories #FOS: Physical sciences #Gauge symmetry #Gauge theory #General Relativity and Quantum Cosmology (gr-qc) #Geometry #High Energy Physics - Theory (hep-th) #Homogeneous space #Mathematics #Other Condensed Matter (cond-mat.other) #Physics #Quantum #Quantum gravity #Quantum mechanics #Solar and Space Plasma Dynamics #Spacetime #Spacetime symmetries #Spontaneous symmetry breaking #Symmetry breaking #Theoretical physics #cond-mat.other #gr-qc #hep-th
paper · pdf · doi:10.48550/arxiv.1501.03845
published in arXiv (Cornell University) (Cornell University) · 58 pages, 1 table, 1 free cut-and-paste project for rainy days in Appendix
arxiv created 2015/01/15 · openalex publication_date 2015/01/15 · arxiv updated 2015/01/19 · openalex created_date 2022/10/05 · openalex updated_date 2026/08/06
We classify condensed matter systems in terms of the spacetime symmetries\nthey spontaneously break. In particular, we characterize condensed matter\nitself as any state in a Poincar 'e-invariant theory that spontaneously breaks\nLorentz boosts while preserving at large distances some form of spatial\ntranslations, time-translations, and possibly spatial rotations. Surprisingly,\nthe simplest, most minimal system achieving this symmetry breaking\npattern---the "framid"---does not seem to be realized in Nature. Instead,\nNature usually adopts a more cumbersome strategy: that of introducing internal\ntranslational symmetries---and possibly rotational ones---and of spontaneously\nbreaking them along with their space-time counterparts, while preserving\nunbroken diagonal subgroups. This symmetry breaking pattern describes the\ninfrared dynamics of ordinary solids, fluids, superfluids, and---if they\nexist---supersolids. A third, "extra-ordinary", possibility involves replacing\nthese internal symmetries with other symmetries that do not commute with the\nPoincar 'e group, for instance the galileon symmetry, supersymmetry or gauge\nsymmetries. Among these options, we pick the systems based on the galileon\nsymmetry, the "galileids", for a more detailed study. Despite some similarity,\nall different patterns produce truly distinct physical systems with different\nobservable properties. For instance, the low-energy 2\→ 2 scattering\namplitudes for the Goldstone excitations in the cases of framids, solids and\ngalileids scale respectively as E2, E4, and E6. Similarly the energy\nmomentum tensor in the ground state is "trivial" for framids (\ρ +p=0),\nnormal for solids (\ρ+p>0) and even inhomogenous for galileids.\n