Phonons as Goldstone Bosons

CERN); H. Leutwyler (University of Bern

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Phonons as Goldstone Bosons

High Energy Physics - Phenomenology · Submitted 25 Sep 1996

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim In particular, I argue that, as a consequence of the hidden symmetry, the equations of motion for a sound wave necessarily contain nonlinear terms, describing phonon-phonon scattering and emphasize the analogy with the low energy theorems for pion-pion scattering.

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What the abstract itself states, as probabilities: claims first 0.04 · states limitation 0.93 · human participants 0.01 · controlled comparison 0.01 · randomized assignment 0.01 · states quantitative result 0.03 · compares with prior results 0.64 · mentions code or data availability 0.01.

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arXiv listing abstract v1. Results and the main claim are underlined; show every role.

The implications of the hidden, spontaneously broken symmetry for the properties of the sound waves of a solid are analyzed. Although the discussion does not go beyond standard wisdom, it presents some of the known results from a different perspective. In particular, I argue that, as a consequence of the hidden symmetry, the equations of motion for a sound wave necessarily contain nonlinear terms, describing phonon-phonon scattering and emphasize the analogy with the low energy theorems for pion-pion scattering.

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#	sentence	role	the authors' own work	states the main conclusion	strength
s0	The implications of the hidden, spontaneously broken symmetry for the properties of the sound waves of a solid are analyzed.	contribution 0.88	0.66	0.10	asserted 0.68
s1	Although the discussion does not go beyond standard wisdom, it presents some of the known results from a different perspective.	limitation 0.97	0.41	0.03	asserted 0.96
s2	In particular, I argue that, as a consequence of the hidden symmetry, the equations of motion for a sound wave necessarily contain nonlinear terms, describing phonon-phonon scattering and emphasize the analogy with the low energy theorems for pion-pion scattering.	result 0.46	0.66	0.85	asserted 0.95

What kind of paper the classifier reports this is: position or commentary 0.58 · evidence from argument 0.93.

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The paper

Original abstract

The implications of the hidden, spontaneously broken symmetry for the properties of the sound waves of a solid are analyzed. Although the discussion does not go beyond standard wisdom, it presents some of the known results from a different perspective. In particular, I argue that, as a consequence of the hidden symmetry, the equations of motion for a sound wave necessarily contain nonlinear terms, describing phonon-phonon scattering and emphasize the analogy with the low energy theorems for pion-pion scattering.

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References

Forward citations

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How later papers used it

55 later papers cite it

Evidence: substantial. 55 of the citing papers share no author with it, and 6 of those carry a confident label from Pith's citation classifier.

Pith read 10 of the 75 citing sentences, choosing only those whose citation markers point at this paper alone, and wrote the paraphrases from them. The summary, the counts, the evidence level, the links and the quotes come from code; the summary counts the papers listed below. A later paper is listed under a label when Pith's citation classifier gives one of its sentences that label at probability 0.8 or more (0.95 for support), Pith's reading finds that the citing paper itself did it, and a second check confirms the paraphrase against the sentence. This section lists uses only. It does not list criticism or disagreement, so their absence here says nothing about how the paper has been received. Papers that share an author with this one are listed apart, under "By the same authors". A quote is the citing authors' own sentence, shown when their paper's licence is CC BY, CC BY-SA or CC0. JSON

1 later paper by other authors is listed below: 1 compared its own results with it.

Compares with it 1 of 2 papers with this label

Compared its own results with this paper.

Black Rubber and the Non-linear Elastic Response of Scale Invariant Solids (2020) · 0.99 · paraphrased: the licence does not allow quoting

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56 arXiv papers cite this in 76 sentences

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

Papers citing it · 46 sentences without a confident label

Builds on it 1 paper

We will, however, guess the form of this action by improving on the previous proposal of Ref. [ref] (see also Ref. [ref] ).

Deconstructing holographic liquids · Ideal hydrodynamics as a theory of Goldstone bosons · 0.96

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In this work we employ an effective field theory (EFT) approach [ref] to describe the interaction between the dark matter and the superfluid phonon.

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We will use the field-theoretical description of fluids introduced in Ref. [ref] , which is based on previous work on the field theory of solids [ref] and supersolids [ref] .

Hall viscosity from effective field theory · Introduction · 0.95
This variable is also more amenable to treat homogeneity and isotropy as an internal symmetry for the scalar fields $Φ^I$, as done in [ref] , which is why the index label on $π^I$ has been capitalized.

Black Rubber and the Non-linear Elastic Response of Scale Invariant Solids · Nonlinear Elastic response · 0.84

Compares with it 2 papers

We can write the 5 $𝒞$'s as a function of these quantities and we would just need two independent new parameters [equation] [equation] [equation] [equation] [equation] where the independent new parameters are [equation] [equation] We can compare our results with Ref. [ref] .

Black Rubber and the Non-linear Elastic Response of Scale Invariant Solids · Three-phonon interaction terms in Solid EFTs · 0.99
This is in close analogy to the phonon as the Goldstone mode of the spontaneously broken Galilean symmetry in fluids [ref] .

Spectral sum rules and phase transition in strongly coupled QCD · Transmutation of degrees of freedom · 0.81

Cites it as background 22 papers

As is well-known, similar statements apply to the spontaneous breaking of spacetime symmetries [ref] , albeit with a fewer number of NGBs than naively expected [ref] .

Soft Phonon Theorems · Introduction · 0.90
The resulting Solid EFT are discussed at lowest order in derivatives for the phonon fields in [ref] , see also [ref] .

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The dynamics of Goldstone modes has already been studied in holography [ref] and field theory [ref] .

Holographic phonons by gauge-axion coupling · Spontaneous breaking of translations · 0.99

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