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Collective excitations in solids, fluids and superfluids are the Goldstone modes of broken spacetime symmetries, and their low-energy dynamics follow from a single effective-field-theory construction.

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2026-07-10 23:45 UTC pith:DRSXT3R3

load-bearing objection Solid, self-contained review that organizes two decades of spacetime-Goldstone EFTs for solids/fluids/superfluids; incremental new thermodynamics and a corrected rate, not a paradigm shift.

arxiv 2607.06666 v1 pith:DRSXT3R3 submitted 2026-07-07 hep-th cond-mat.otherhep-ph

Effective Field Theories for Material Media

Angelo Esposito , Alberto Nicolis , Riccardo Penco This is my paper
classification hep-th cond-mat.otherhep-ph
keywords effective field theoryGoldstone bosonsspontaneous symmetry breakingsolidsfluidssuperfluidshydrodynamicsSchwinger–Keldysh
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

This review shows that the mechanical degrees of freedom of ordinary solids, fluids and superfluids can be written as effective field theories for the Goldstone modes that appear when boosts, translations and rotations are spontaneously broken by a finite-density medium. The only ingredients are the unbroken residual symmetries and a derivative expansion; once those are fixed, the entire low-energy action is determined up to a few thermodynamic functions. Phonons, sound waves, vorticity and superfluid phonons then emerge as the same universal objects, with their speeds, interactions and transport coefficients fixed by the same symmetry algebra. The construction also supplies a clean non-relativistic limit and a systematic way to include dissipation through the Schwinger–Keldysh formalism. A reader who works with either high-energy or condensed-matter methods therefore gains a single language in which mechanical deformations, hydrodynamics and superfluidity become special cases of the same Goldstone dynamics.

Core claim

At long distances the continuum limit of any homogeneous medium is completely described by the Goldstone effective action that realises the spontaneous breaking of Poincaré symmetries (boosts, spatial translations, rotations) together with the appropriate internal shift and diffeomorphism symmetries; all bulk and localised collective excitations, their dispersion relations and their leading interactions are then fixed by that action and its derivative expansion.

What carries the argument

The coset/Goldstone effective action for spontaneously broken spacetime symmetries, written in terms of comoving scalar fields (or their Clebsch/Lagrangian duals) whose residual symmetries encode the continuum limit of the medium; a single derivative expansion then generates the entire low-energy dynamics, including the non-relativistic scaling limit and the Schwinger–Keldysh extension that incorporates dissipation.

Load-bearing premise

The continuum, long-wavelength limit is assumed to restore continuous residual translations even when the microscopic lattice is discrete, so that any operators that would break those continuous translations are non-perturbative and can be dropped to all orders in the derivative expansion.

What would settle it

A controlled lattice calculation or experiment that finds a relevant higher-derivative operator (or a measurable correction to phonon dispersion or scattering) that cannot be absorbed into the continuum Goldstone action and that survives in the infinite-wavelength limit would falsify the claim that continuous residual translations are exact to all orders in the derivative expansion.

Watch this falsifier — get emailed when new claim-graph text bears on it.

If this is right

  • Phonon and sound-wave scattering rates, including the classic k^5 decay of superfluid phonons, become universal predictions of a few thermodynamic derivatives of the effective Lagrangian.
  • Viscosity, conductivity and other first-order transport coefficients are fixed by the same Wilson coefficients that appear in the Schwinger–Keldysh effective action, with positivity following from unitarity rather than being imposed by hand.
  • The non-relativistic limit is obtained by a well-defined scaling of the relativistic action, automatically producing Galilean-invariant kinetic terms and the correct mass density without additional assumptions.
  • A symmetry-based classification of media (type-I/II superfluids, supersolids, Galileids, framids) follows directly from which generators remain unbroken, predicting new phases whose Goldstone content can be written down at once.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The same construction should supply a controlled effective theory for electron–phonon or magnon–phonon systems once the additional low-energy fields are coupled to the solid’s comoving coordinates.
  • Because the continuum residual translations are claimed to be exact to all orders in derivatives, any lattice-sensitive correction to long-wavelength phonon physics would have to be non-perturbative in the lattice spacing—an experimentally sharp statement for cold-atom or photonic crystals.
  • The Schwinger–Keldysh formulation already contains the noise that realises the fluctuation–dissipation theorem; the same action can therefore be used as a first-principles generator of stochastic hydrodynamics without extra phenomenological input.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit.

Referee Report

0 major / 4 minor

Summary. This review constructs and unifies effective field theories for the mechanical degrees of freedom of solids, fluids and superfluids from the spontaneous breaking of spacetime symmetries (boosts, translations, rotations) together with appropriate internal symmetries. The solid EFT is built from three comoving scalars φ^I with shift and discrete rotational symmetries, yielding an action F(B^{IJ}) whose thermodynamics and phonon spectrum recover continuum elasticity; fluids are obtained by imposing volume-preserving diffeomorphisms, with several equivalent Eulerian/Lagrangian formulations and a full Schwinger–Keldysh treatment of first-order viscosity; superfluids are described by the classic P(X) action for a U(1) Goldstone, from which phonon decay rates and the non-relativistic limit follow. Non-relativistic limits are systematically obtained as a scaling limit, and a symmetry-based classification of further phases (supersolids, Galileids, framids) is sketched. The central claim is that the low-energy mechanical dynamics of these media are completely captured by the resulting Goldstone actions, with transport coefficients and scattering rates fixed by a controlled derivative expansion.

Significance. If the constructions hold, the paper supplies a single, symmetry-first language that recovers standard continuum elasticity, perfect-fluid hydrodynamics and superfluid phonon physics while making the non-linear realization of Lorentz invariance and the origin of transport coefficients transparent. Explicit strengths include: (i) the thermodynamic identification of the solid and fluid Lagrangians (Secs. 3.3, 4.2); (ii) the complete Schwinger–Keldysh derivation of bulk and shear viscosities together with positivity from unitarity (Sec. 4.6); (iii) the corrected roton–phonon scattering rate and the systematic non-relativistic scaling limit; and (iv) a pedagogical bridge between high-energy and condensed-matter communities. These are genuine computational and conceptual advances for anyone working on Goldstone EFTs of media, holographic duals, or cosmological applications of solids/fluids.

minor comments (4)
  1. [Sec. 5.3] The manuscript is truncated mid-sentence in Sec. 5.3 (after Eq. (5.52)); the published version should restore the missing text on higher-derivative corrections and the subsequent subsections on finite-temperature superfluids, vortices and rotons.
  2. [Sec. 6] A short table or schematic summarizing the residual unbroken generators for solids, fluids, type-I/II superfluids, supersolids, Galileids and framids would make Sec. 6 more immediately usable.
  3. A few typographical inconsistencies remain (e.g., “almot” for “almost” near Eq. (4.16), occasional missing spaces around citations). A final copy-edit pass would remove them.
  4. [Sec. 2.1] The discussion of inverse-Higgs constraints (Sec. 2.1) could briefly point the reader to the modern literature on counting rules for spacetime Goldstones, even if the coset construction is not used in the body.

Circularity Check

1 steps flagged

No significant circularity: symmetry-based EFT constructions recover standard continuum hydrodynamics/elasticity with free Wilson coefficients; self-citations are to prior technical derivations, not load-bearing uniqueness claims that force the results.

specific steps
  1. self citation load bearing [§2.1 (Continuous Media) and citation [20]]
    "it can be proved that in the long-distance effective theory there is no difference between discrete translations with microscopic spacing and continuous translations to all orders in the derivative expansion [20]. From the viewpoint of the derivative expansion, the difference is non-perturbative."

    The continuum restoration of unbroken continuous residual translations (needed for the homogeneous solid/fluid EFTs) is justified by a citation that is part of the authors' prior technical line. The claim is standard continuum elasticity/hydrodynamics and is not used to force any numerical prediction or uniqueness of the actions themselves; it is a minor supporting assumption rather than a load-bearing circular step for the central Goldstone constructions.

full rationale

The paper is a pedagogical review that builds Goldstone EFTs for solids (three scalars with internal shifts + G), fluids (volume-preserving diffeos, or 3/4-field Eulerian/Lagrangian equivalents), and superfluids (U(1) phase with finite density) from spacetime + internal symmetries, then expands to phonons, thermodynamics, transport, and scattering. Stress-energy tensors and constitutive relations are derived from the actions (e.g. Tµν from Noether/metric variation) and matched to standard thermo/hydro; Wilson coefficients (sound speeds, gi, viscosities, gn) remain free parameters to be fixed by experiment or UV matching, not fitted to produce the target observables. Positivity of viscosities follows from unitarity of the SK action, not from assuming the second law. Continuum restoration of residual translations is the usual long-wavelength assumption (explicitly noted as non-perturbative in the derivative expansion). Self-citations (e.g. [19,20,91,98]) point to earlier constructions of the same actions; they are not used as external uniqueness theorems that forbid alternatives or smuggle ansatze. No fitted-input-as-prediction, self-definitional loops, or renaming of known empirical patterns as new first-principles results. Minor residual self-citation load is present but not central; score 1 reflects that alone.

Axiom & Free-Parameter Ledger

0 free parameters · 4 axioms · 0 invented entities

The central claims rest on standard QFT axioms (Lorentz invariance of the UV theory, Goldstone theorem for spontaneously broken continuous symmetries, derivative expansion) plus the domain assumption that the continuum limit restores continuous residual translations. No free parameters are fitted; the Wilson coefficients of the EFTs remain free. No new entities are postulated.

axioms (4)
  • domain assumption Lorentz (or Galilei) invariance of the microscopic theory is spontaneously broken by the medium’s ground state or density matrix.
    Stated in §1 and used throughout to justify the existence of Goldstone fields.
  • domain assumption In the long-wavelength limit discrete lattice translations become continuous residual translations to all orders in the derivative expansion.
    Invoked in §2.1 and justified by reference to [20]; without it the solid EFT would contain non-perturbative breaking terms.
  • standard math Goldstone theorem and inverse-Higgs constraints for spacetime symmetries.
    Standard results used to count independent fields (§2.1).
  • domain assumption Schwinger–Keldysh doubling plus KMS symmetry correctly encodes dissipation and fluctuation–dissipation relations.
    Adopted in §4.6 as the framework for imperfect fluids.

pith-pipeline@v1.1.0-grok45 · 62912 in / 2219 out tokens · 31095 ms · 2026-07-10T23:45:41.036203+00:00 · methodology

0 comments
read the original abstract

We review recent progress in understanding certain aspects of condensed matter systems from a high energy theory perspective. We discuss effective field theories that describe collective bulk and localized excitations in a variety of solid and fluid systems. Particular emphasis is placed on the role played by spacetime symmetries and their spontaneous breaking. The resulting Goldstone dynamics can be seen as underlying a wide variety of phenomena. We attempt to bridge the language gap between subfields while underscoring the numerous conceptual similarities.

Figures

Figures reproduced from arXiv: 2607.06666 by Alberto Nicolis, Angelo Esposito, Riccardo Penco.

Figure 1
Figure 1. Figure 1: The equilibrium configuration (dashed line) of a string in two spatial dimensions spontaneously breaks three [PITH_FULL_IMAGE:figures/full_fig_p009_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Left panel: Relation between physical and comoving coordinates for a solid at equilibrium, Eq. (3.2). Right panel: Same relation but for a solid slightly away from equilibrium, Eq. (3.34). spacetime symmetries: Lorentz boosts, rotations, and, most importantly, spatial translations. On the other hand, we would like the equilibrium state of our continuous solid to be homogeneous, that is, translationally inv… view at source ↗
Figure 3
Figure 3. Figure 3: Measured spectrum of collective modes in superfluid [PITH_FULL_IMAGE:figures/full_fig_p073_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Parametrization of the vortex line configuration, [PITH_FULL_IMAGE:figures/full_fig_p079_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Experimental image of a vortex lattice featuring a Tkachenko mode (black lines), as reported in [ [PITH_FULL_IMAGE:figures/full_fig_p084_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Different phases of superfluid 3He. Red solid arrows represent the atomic spin, S⃗, while blue dashed arrows the atomic orbital angular momentum, L⃗ . Left panel: A-phase. The directions of both S⃗ and L⃗ are fixed. Right panel: B-phase. The relative angle between S⃗ and L⃗ is fixed, but their overall orientation is random. As anticipated, type-II superfluids do exist in Nature. A nonrelativistic realizati… view at source ↗
Figure 7
Figure 7. Figure 7: Possible trajectories of rotons under gravitational acceleration [PITH_FULL_IMAGE:figures/full_fig_p107_7.png] view at source ↗

discussion (0)

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Reference graph

Works this paper leans on

294 extracted references · 294 canonical work pages · 195 internal anchors

  1. [1]

    Weinberg, The Quantum theory of fields

    S. Weinberg, The Quantum theory of fields. Vol. 1: Foundations, Cambridge University Press, 2005.doi:10.1017/CBO9781139644167

    work page doi:10.1017/cbo9781139644167 2005

  2. [2]

    Zoology of condensed matter: Framids, ordinary stuff, extra-ordinary stuff

    A. Nicolis, R. Penco, F. Piazza, R. Rattazzi, Zoology of condensed matter: Framids, or- dinary stuff, extra-ordinary stuff, JHEP 06 (2015) 155. arXiv:1501.03845, doi:10.1007/ JHEP06(2015)155

    work page internal anchor Pith review Pith/arXiv arXiv 2015

  3. [3]

    Strocchi, Symmetry Breaking, Vol

    F. Strocchi, Symmetry Breaking, Vol. 9783662621660, Springer, 2021. doi:10.1007/ 978-3-662-62166-0

    work page 2021

  4. [4]

    H. J. Maris, Phonon-phonon interactions in liquid helium, Reviews of Modern Physics 49 (2) (1977) 341.doi:10.1103/RevModPhys.49.341

    work page doi:10.1103/revmodphys.49.341 1977

  5. [5]

    Morchio, F

    G. Morchio, F. Strocchi, Spontaneous Breaking of the Galilei Group and the Plasmon Energy Gap, Annals Phys. 170 (1986) 310.doi:10.1016/0003-4916(86)90095-3

    work page doi:10.1016/0003-4916(86)90095-3 1986

  6. [6]

    Ojima, Lorentz Invariance Versus Temperature in QFT, Lett

    I. Ojima, Lorentz Invariance Versus Temperature in QFT, Lett. Math. Phys. 11 (1986) 73. doi:10.1007/BF00417467

    work page doi:10.1007/bf00417467 1986

  7. [7]

    Spontaneous Symmetry Breaking of Lorentz and (Galilei) Boosts in (Relativistic) Many-Body Systems

    M. Requardt, Spontaneous Symmetry Breaking of Lorentz and (Galilei) Boosts in (Relativistic) Many-Body SystemsarXiv:0805.3022

    work page internal anchor Pith review Pith/arXiv arXiv

  8. [8]

    Spontaneously broken boosts and the Goldstone continuum

    L. Alberte, A. Nicolis, Spontaneously broken boosts and the Goldstone continuum, JHEP 07 (2020) 076.arXiv:2001.06024,doi:10.1007/JHEP07(2020)076

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1007/jhep07(2020)076 2020

  9. [9]

    E. A. Ivanov, V. I. Ogievetsky, The Inverse Higgs Phenomenon in Nonlinear Realizations, Teor. Mat. Fiz. 25 (1975) 164–177.doi:10.1007/BF01028947

    work page doi:10.1007/bf01028947 1975

  10. [10]

    I. Low, A. V. Manohar, Spontaneously broken space-time symmetries and Goldstone’s theorem, Phys. Rev. Lett. 88 (2002) 101602. arXiv:hep-th/0110285, doi:10.1103/PhysRevLett.88. 101602

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1103/physrevlett.88 2002

  11. [11]

    I. N. McArthur, Nonlinear realizations of symmetries and unphysical Goldstone bosons, JHEP 11 (2010) 140.arXiv:1009.3696,doi:10.1007/JHEP11(2010)140

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1007/jhep11(2010)140 2010

  12. [12]

    More on gapped Goldstones at finite density: More gapped Goldstones

    A. Nicolis, R. Penco, F. Piazza, R. A. Rosen, More on gapped Goldstones at finite density: More gapped Goldstones, JHEP 11 (2013) 055. arXiv:1306.1240, doi:10.1007/JHEP11(2013)055

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1007/jhep11(2013)055 2013

  13. [13]

    Redundancies in Nambu-Goldstone Bosons

    H. Watanabe, H. Murayama, Redundancies in Nambu-Goldstone Bosons, Phys. Rev. Lett. 110 (18) (2013) 181601.arXiv:1302.4800,doi:10.1103/PhysRevLett.110.181601

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1103/physrevlett.110.181601 2013

  14. [14]

    S. R. Coleman, J. Wess, B. Zumino, Structure of phenomenological Lagrangians. 1., Phys. Rev. 177 (1969) 2239–2247.doi:10.1103/PhysRev.177.2239

    work page doi:10.1103/physrev.177.2239 1969

  15. [15]

    C. G. Callan, Jr., S. R. Coleman, J. Wess, B. Zumino, Structure of phenomenological Lagrangians. 2., Phys. Rev. 177 (1969) 2247–2250.doi:10.1103/PhysRev.177.2247

    work page doi:10.1103/physrev.177.2247 1969

  16. [16]

    V. I. Ogievetsky, Nonlinear realizations of internal and space-time symmetries, Proceedings of the Xth winter school of theoretical physics in Karpacz 1 (1974) 117

    work page 1974

  17. [17]

    L. V. Delacr´ etaz, S. Endlich, A. Monin, R. Penco, F. Riva, (Re-)Inventing the Relativistic Wheel: Gravity, Cosets, and Spinning Objects, JHEP 11 (2014) 008. arXiv:1405.7384, doi:10.1007/JHEP11(2014)008. 120

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1007/jhep11(2014)008 2014

  18. [18]

    L. D. Landau, E. M. Lifshitz, Theory of Elasticity, Vol. 7 of Course of Theoretical Physics, Elsevier Butterworth-Heinemann, New York, 1986.doi:10.1016/C2009-0-25521-8

    work page doi:10.1016/c2009-0-25521-8 1986

  19. [19]

    Soper, Classical Field Theory, Dover Books on Physics, Dover Publications, 2008

    D. Soper, Classical Field Theory, Dover Books on Physics, Dover Publications, 2008

    work page 2008

  20. [20]

    Solidity without inhomogeneity: Perfectly homogeneous, weakly coupled, UV-complete solids

    A. Esposito, R. Krichevsky, A. Nicolis, Solidity without inhomogeneity: Perfectly homogeneous, weakly coupled, UV-complete solids, JHEP 11 (2020) 021. arXiv:2004.11386, doi:10.1007/ JHEP11(2020)021

    work page internal anchor Pith review Pith/arXiv arXiv 2020

  21. [21]

    L. D. Landau, E. M. Lifshitz, Statistical Physics, Part 1, Vol. 5 of Course of Theoretical Physics, Butterworth-Heinemann, Oxford, 1980.doi:10.1016/C2009-0-24487-4

    work page doi:10.1016/c2009-0-24487-4 1980

  22. [22]

    M. I. Aroyo, et al., International tables for crystallography volume a: Space-group symmetry, In- ternational Tables for Crystallography (2016) 193–687 doi:10.1107/97809553602060000001

    work page doi:10.1107/97809553602060000001 2016

  23. [23]

    Levine, P

    D. Levine, P. J. Steinhardt, Quasicrystals: a new class of ordered structures, Physical review letters 53 (26) (1984) 2477.doi:10.1103/PhysRevLett.53.2477

    work page doi:10.1103/physrevlett.53.2477 1984

  24. [24]

    Solid Inflation

    S. Endlich, A. Nicolis, J. Wang, Solid Inflation, JCAP 10 (2013) 011. arXiv:1210.0569, doi:10.1088/1475-7516/2013/10/011

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1088/1475-7516/2013/10/011 2013

  25. [25]

    J. Kang, A. Nicolis, Platonic solids back in the sky: Icosahedral inflation, JCAP 03 (2016) 050.arXiv:1509.02942,doi:10.1088/1475-7516/2016/03/050

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1088/1475-7516/2016/03/050 2016

  26. [26]

    J. Kang, A. Nicolis, Anisotropic tensor modes from icosahedral inflation. arXiv:1807.03924

    work page internal anchor Pith review Pith/arXiv arXiv

  27. [27]

    Scalar-tensor mixing from icosahedral inflation

    A. Nicolis, G. Sun, Scalar-tensor mixing from icosahedral inflation, JCAP 04 (2021) 074. arXiv:2011.04687,doi:10.1088/1475-7516/2021/04/074

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1088/1475-7516/2021/04/074 2021

  28. [28]

    Weinberg, Gravitation and Cosmology: Principles and Applications of the General Theory of Relativity, John Wiley and Sons, New York, 1972

    S. Weinberg, Gravitation and Cosmology: Principles and Applications of the General Theory of Relativity, John Wiley and Sons, New York, 1972

    work page 1972

  29. [29]

    Weinberg, Cosmology, Oxford University Press, 2008

    S. Weinberg, Cosmology, Oxford University Press, 2008

    work page 2008

  30. [30]

    Phonons as Goldstone Bosons

    H. Leutwyler, Phonons as goldstone bosons, Helv. Phys. Acta 70 (1997) 275–286. arXiv: hep-ph/9609466

    work page internal anchor Pith review Pith/arXiv arXiv 1997

  31. [31]

    Energy conditions in general relativity and quantum field theory

    E.-A. Kontou, K. Sanders, Energy conditions in general relativity and quantum field theory, Class. Quant. Grav. 37 (19) (2020) 193001. arXiv:2003.01815, doi:10.1088/1361-6382/ ab8fcf

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1088/1361-6382/ 2020

  32. [32]

    The squeezed limit of the solid inflation three-point function

    S. Endlich, B. Horn, A. Nicolis, J. Wang, Squeezed limit of the solid inflation three-point function, Phys. Rev. D 90 (6) (2014) 063506. arXiv:1307.8114, doi:10.1103/PhysRevD.90. 063506

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1103/physrevd.90 2014

  33. [33]

    An Effective Field Theory of Magneto-Elasticity

    S. Pavaskar, R. Penco, I. Z. Rothstein, An effective field theory of magneto-elasticity, SciPost Phys. 12 (5) (2022) 155.arXiv:2112.13873,doi:10.21468/SciPostPhys.12.5.155

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.21468/scipostphys.12.5.155 2022

  34. [34]

    L. D. Landau, J. S. Bell, M. Kearsley, L. Pitaevskii, E. Lifshitz, J. Sykes, Electrodynamics of continuous media, Vol. 8, elsevier, 2013

    work page 2013

  35. [35]

    M. Born, E. Wolf, Principles of optics, Cambridge Univ. Pr., 1999. doi:10.1017/ CBO9781139644181. 121

    work page 1999

  36. [36]

    Scheibner, A

    C. Scheibner, A. Souslov, D. Banerjee, P. Sur´ owka, W. T. Irvine, V. Vitelli, Odd elasticity, Nature Physics 16 (4) (2020) 475–480.doi:10.1038/s41567-020-0795-y

    work page doi:10.1038/s41567-020-0795-y 2020

  37. [37]

    Andreev, I

    A. Andreev, I. Lifshits, Quantum theory of defects in crystals, Zhur Eksper Teoret Fiziki 56 (6) (1969) 2057–2068

    work page 1969

  38. [38]

    Chester, Speculations on bose-einstein condensation and quantum crystals, Physical Review A 2 (1) (1970) 256.doi:10.1103/PhysRevA.2.256

    G. Chester, Speculations on bose-einstein condensation and quantum crystals, Physical Review A 2 (1) (1970) 256.doi:10.1103/PhysRevA.2.256

    work page doi:10.1103/physreva.2.256 1970

  39. [39]

    superfluid

    A. J. Leggett, Can a solid be “superfluid”?, Phys. Rev. Lett. 25 (1970) 1543–1546. doi: 10.1103/PhysRevLett.25.1543

    work page doi:10.1103/physrevlett.25.1543 1970

  40. [40]

    D. T. Son, Effective Lagrangian and topological interactions in supersolids, Phys. Rev. Lett. 94 (2005) 175301.arXiv:cond-mat/0501658,doi:10.1103/PhysRevLett.94.175301

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1103/physrevlett.94.175301 2005

  41. [41]

    Effective Field Theory for Spontaneously Broken Symmetry

    T. Brauner, Effective Field Theory for Spontaneously Broken Symmetry, Lect. Notes Phys. 1023 (2024) pp.arXiv:2404.14518,doi:10.1007/978-3-031-48378-3

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1007/978-3-031-48378-3 2024

  42. [42]

    Levine, P

    D. Levine, P. J. Steinhardt, Quasicrystals. i. definition and structure, Physical Review B 34 (2) (1986) 596.doi:10.1103/PhysRevB.34.596

    work page doi:10.1103/physrevb.34.596 1986

  43. [43]

    J. E. Socolar, P. J. Steinhardt, Quasicrystals. ii. unit-cell configurations, Physical Review B 34 (2) (1986) 617.doi:10.1103/PhysRevB.34.617

    work page doi:10.1103/physrevb.34.617 1986

  44. [44]

    Effective Field Theory for Quasicrystals and Phasons Dynamics

    M. Baggioli, M. Landry, Effective Field Theory for Quasicrystals and Phasons Dynamics, SciPost Phys. 9 (5) (2020) 062.arXiv:2008.05339,doi:10.21468/SciPostPhys.9.5.062

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.21468/scipostphys.9.5.062 2020

  45. [45]

    Deformations, relaxation and broken symmetries in liquids, solids and glasses: a unified topological field theory

    M. Baggioli, M. Landry, A. Zaccone, Deformations, relaxation, and broken symmetries in liquids, solids, and glasses: A unified topological field theory, Phys. Rev. E 105 (2) (2022) 024602.arXiv:2101.05015,doi:10.1103/PhysRevE.105.024602

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1103/physreve.105.024602 2022

  46. [46]

    M. J. Landry, Active actions: Effective field theory for active nematics.arXiv:2309.15142

    work page internal anchor Pith review Pith/arXiv arXiv

  47. [47]

    Effective Field Theory and the Fermi Surface

    J. Polchinski, Effective field theory and the fermi surface.arXiv:hep-th/9210046

    work page internal anchor Pith review Pith/arXiv arXiv

  48. [48]

    Renormalization Group Approach to Interacting Fermions

    R. Shankar, Renormalization group approach to interacting fermions, Rev. Mod. Phys. 66 (1994) 129–192.arXiv:cond-mat/9307009,doi:10.1103/RevModPhys.66.129

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1103/revmodphys.66.129 1994

  49. [49]

    Giustino, Electron-phonon interactions from first principles, Reviews of Modern Physics 89 (1) (2017) 015003.doi:10.1103/RevModPhys.89.015003

    F. Giustino, Electron-phonon interactions from first principles, Reviews of Modern Physics 89 (1) (2017) 015003.doi:10.1103/RevModPhys.89.015003

    work page doi:10.1103/revmodphys.89.015003 2017

  50. [50]

    An effective field theory of damped ferromagnetic systems

    J. Li, An effective field theory of damped ferromagnetic systems.arXiv:2312.13093

    work page internal anchor Pith review Pith/arXiv arXiv

  51. [51]

    Chester, Second sound in solids, Phys

    M. Chester, Second sound in solids, Phys. Rev. 131 (5) (1963) 2013. doi:10.1103/PhysRev. 131.2013

    work page doi:10.1103/physrev 1963

  52. [52]

    Guyer, J

    R. Guyer, J. Krumhansl, Dispersion relation for second sound in solids, Physical Review 133 (5A) (1964) A1411.doi:10.1103/PhysRev.133.A1411

    work page doi:10.1103/physrev.133.a1411 1964

  53. [53]

    R. N. Gurzhi, Second sound in solids, Sov. Phys. Solid State 7 (12) (1965) 2838–2842

    work page 1965

  54. [54]

    L. P. Pitaevskii, Second sound in solids, Soviet Physics Uspekhi 11 (3) (1968) 342–344

    work page 1968

  55. [55]

    M. J. Landry, Non-equilibrium effective field theory and second sound, JHEP 04 (2021) 213. arXiv:2008.11725,doi:10.1007/JHEP04(2021)213. 122

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1007/jhep04(2021)213 2021

  56. [56]

    Higgs and Goldstone modes in crystalline solids

    M. Vallone, Higgs and Goldstone Modes in Crystalline Solids, Phys. Status Solidi B 257 (3) (2020) 1900443.arXiv:1908.00918,doi:10.1002/pssb.201900443

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1002/pssb.201900443 2020

  57. [57]

    Effective Field Theory for Acoustic and Pseudo-Acoustic Phonons in Solids

    A. Esposito, E. Geoffray, T. Melia, Effective field theory for acoustic and pseudoacoustic phonons in solids, Phys. Rev. D 102 (10) (2020) 105009. arXiv:2006.05429, doi:10.1103/ PhysRevD.102.105009

    work page internal anchor Pith review Pith/arXiv arXiv 2020

  58. [58]

    Kleinert, Gauge Fields in Condensed Matter: Vol

    H. Kleinert, Gauge Fields in Condensed Matter: Vol. 1: Superflow and Vortex Lines (Disorder Fields, Phase Transitions) Vol. 2: Stresses and Defects (Differential Geometry, Crystal Melting), World Scientific, 1989

    work page 1989

  59. [59]

    J.-Y. Lin, I. Z. Rothstein, S. Pavaskar, Dispersion relations for dislocation modes and their sensitivity to the lattice structure, Phys. Rev. B 112 (18) (2025) 184316. arXiv:2212.10587, doi:10.1103/56v8-sh8z

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1103/56v8-sh8z 2025

  60. [60]

    Pretko, L

    M. Pretko, L. Radzihovsky, Fracton-elasticity duality, Physical review letters 120 (19) (2018) 195301.doi:10.1103/PhysRevLett.120.195301ExportCitation

    work page doi:10.1103/physrevlett.120.195301exportcitation 2018

  61. [61]

    Fracton Phases of Matter

    M. Pretko, X. Chen, Y. You, Fracton Phases of Matter, Int. J. Mod. Phys. A 35 (06) (2020) 2030003.arXiv:2001.01722,doi:10.1142/S0217751X20300033

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1142/s0217751x20300033 2020

  62. [62]

    The gravitational mass carried by sound waves

    A. Esposito, R. Krichevsky, A. Nicolis, Gravitational Mass Carried by Sound Waves, Phys. Rev. Lett. 122 (8) (2019) 084501.arXiv:1807.08771,doi:10.1103/PhysRevLett.122.084501

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1103/physrevlett.122.084501 2019

  63. [63]

    Distinctive signatures of space-time diffeomorphism breaking in EFT of inflation

    N. Bartolo, D. Cannone, A. Ricciardone, G. Tasinato, Distinctive signatures of space-time diffeomorphism breaking in EFT of inflation, JCAP 03 (2016) 044. arXiv:1511.07414, doi:10.1088/1475-7516/2016/03/044

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1088/1475-7516/2016/03/044 2016

  64. [64]

    Evolution of perturbations in a universe with exotic solid-like matter

    P. M´ esz´ aros, Evolution of perturbations in a universe with exotic solid-like matter, Phys. Dark Univ. 42 (2023) 101297.arXiv:2302.14480,doi:10.1016/j.dark.2023.101297

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1016/j.dark.2023.101297 2023

  65. [65]

    Is the Dark Matter a Solid?

    M. Bucher, D. N. Spergel, Is the dark matter a solid?, Phys. Rev. D 60 (1999) 043505. arXiv:astro-ph/9812022,doi:10.1103/PhysRevD.60.043505

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1103/physrevd.60.043505 1999

  66. [66]

    P. Cox, T. Melia, S. Rajendran, Dark matter phonon coupling, Phys. Rev. D 100 (5) (2019) 055011.arXiv:1905.05575,doi:10.1103/PhysRevD.100.055011

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1103/physrevd.100.055011 2019

  67. [67]

    Multi-Channel Direct Detection of Light Dark Matter: Theoretical Framework

    T. Trickle, Z. Zhang, K. M. Zurek, K. Inzani, S. M. Griffin, Multi-Channel Direct Detection of Light Dark Matter: Theoretical Framework, JHEP 03 (2020) 036. arXiv:1910.08092, doi:10.1007/JHEP03(2020)036

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1007/jhep03(2020)036 2020

  68. [68]

    Effective Field Theory of Dark Matter Direct Detection With Collective Excitations

    T. Trickle, Z. Zhang, K. M. Zurek, Effective field theory of dark matter direct detection with collective excitations, Phys. Rev. D 105 (1) (2022) 015001. arXiv:2009.13534, doi: 10.1103/PhysRevD.105.015001

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1103/physrevd.105.015001 2022

  69. [69]

    Effective Field Theory for Dark Matter Absorption on Single Phonons

    A. Mitridate, K. Pardo, T. Trickle, K. M. Zurek, Effective field theory for dark matter absorption on single phonons, Phys. Rev. D 109 (1) (2024) 015010. arXiv:2308.06314, doi:10.1103/PhysRevD.109.015010

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1103/physrevd.109.015010 2024

  70. [70]

    Conformal solids and holography

    A. Esposito, S. Garcia-Saenz, A. Nicolis, R. Penco, Conformal solids and holography, JHEP 12 (2017) 113.arXiv:1708.09391,doi:10.1007/JHEP12(2017)113

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1007/jhep12(2017)113 2017

  71. [71]

    Scale invariant solids

    M. Baggioli, V. C. Castillo, O. Pujolas, Scale invariant solids, Phys. Rev. D 101 (8) (2020) 086005.arXiv:1910.05281,doi:10.1103/PhysRevD.101.086005. 123

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1103/physrevd.101.086005 2020

  72. [72]

    Black Rubber and the Non-linear Elastic Response of Scale Invariant Solids

    M. Baggioli, V. C. Castillo, O. Pujolas, Black Rubber and the Non-linear Elastic Response of Scale Invariant Solids, JHEP 09 (2020) 013. arXiv:2006.10774, doi:10.1007/JHEP09(2020) 013

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1007/jhep09(2020 2020

  73. [74]

    Diffusion and universal relaxation of holographic phonons

    A. Amoretti, D. Are´ an, B. Gout´ eraux, D. Musso, Diffusion and universal relaxation of holographic phonons, JHEP 10 (2019) 068. arXiv:1904.11445, doi:10.1007/JHEP10(2019) 068

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1007/jhep10(2019 2019

  74. [75]

    Zoology of Solid & Fluid Holography : Goldstone Modes and Phase Relaxation

    M. Baggioli, S. Grieninger, Zoology of solid \& fluid holography — Goldstone modes and phase relaxation, JHEP 10 (2019) 235. arXiv:1905.09488, doi:10.1007/JHEP10(2019)235

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1007/jhep10(2019)235 2019

  75. [76]

    Viscoelastic hydrodynamics and holography

    J. Armas, A. Jain, Viscoelastic hydrodynamics and holography, JHEP 01 (2020) 126. arXiv: 1908.01175,doi:10.1007/JHEP01(2020)126

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1007/jhep01(2020)126 2020

  76. [77]

    Gapless and gapped holographic phonons

    A. Amoretti, D. Are´ an, B. Gout´ eraux, D. Musso, Gapless and gapped holographic phonons, JHEP 01 (2020) 058.arXiv:1910.11330,doi:10.1007/JHEP01(2020)058

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1007/jhep01(2020)058 2020

  77. [78]

    L.-Z. Xia, L. Xu, W.-J. Li, Collective dynamics in holographic fractonic solids, JHEP 02 (2026) 089.arXiv:2510.17404,doi:10.1007/JHEP02(2026)089

    work page doi:10.1007/jhep02(2026)089 2026

  78. [79]

    Elasticity bounds from Effective Field Theory

    L. Alberte, M. Baggioli, V. C. Castillo, O. Pujolas, Elasticity bounds from Effective Field Theory, Phys. Rev. D 100 (6) (2019) 065015, [Erratum: Phys.Rev.D 102, 069901 (2020)]. arXiv:1807.07474,doi:10.1103/PhysRevD.100.065015

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1103/physrevd.100.065015 2019

  79. [80]

    Simplest phonons and pseudo-phonons in field theory

    D. Musso, Simplest phonons and pseudo-phonons in field theory, Eur. Phys. J. C 79 (12) (2019) 986.arXiv:1810.01799,doi:10.1140/epjc/s10052-019-7498-5

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1140/epjc/s10052-019-7498-5 2019

  80. [81]

    Phonon and Shifton from a Real Modulated Scalar

    D. Musso, D. Naegels, Independent Goldstone modes for translations and shift symmetry from a real modulated scalar, Phys. Rev. D 101 (4) (2020) 045016. arXiv:1907.04069, doi:10.1103/PhysRevD.101.045016

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1103/physrevd.101.045016 2020

Showing first 80 references.