General coordinate invariance and conformal invariance in nonrelativistic physics: Unitary Fermi gas

D.T. Son; M. Wingate

REVIEW

General coordinate invariance and conformal invariance in nonrelativistic physics: Unitary Fermi gas

D.T. Son, M. Wingate

Other Condensed Matter · Submitted 29 Sep 2005 · 28 references

Pith's verdict: The paper that turned nonrelativistic general coordinate invariance into a working tool, with a two-constant NLO Lagrangian that has held up; the completeness of the NLO basis is asserted rather than proved, but the obvious counterexample collapses.

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CitationD.T. Son, M. Wingate. "General coordinate invariance and conformal invariance in nonrelativistic physics: Unitary Fermi gas." arXiv:cond-mat/0509786 (2005). https://pith.science/paper/3EIOTX3V

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Son and Wingate is the paper that made nonrelativistic general coordinate invariance a usable constraint rather than a curiosity, and the NLO Lagrangian with two constants is the result people actually cite. Worth your time, and worth a real referee if it came in cold today. The new content is the transformation (17), the conformal argument in Sec. 4 that the unitary gas is conformally invariant at infinite scattering length, and the reduction of the NLO basis to c1 and c2 in Eq. 115. The leading-order Lagrangian is Greiter-Wilczek-Witten [15], and they say so. What they add is the curved-space machinery that constrains the next order. The derivation is checkable: the xi-dot cancellation in (17) is shown explicitly, the c3 = -9c2 reduction is carried through in Eqs. 108-114, and the applications (phonon dispersion, chi(q), chi_T(q), trap energy) are worked out cleanly. Eq. 8 is the real payoff, a relation among observables that holds for any c1, c2. That is a genuine prediction, not a fit. On soft spots, the reader's main worry is right in kind but overstated in degree. Sec. 6.2 lifts the NLO basis from the relativistic theory and does not prove the converse, that every nonrelativistic GCI scalar at O(p^2) descends from a relativistic one. The relativistic diffeo group is larger, so the lift is one-directional. But the obvious candidate, (nabla^2 X) f(X), integrates by parts into the L1 structure of Eq. 99, so there is no known counterexample. It is a rigor gap, not an error, and the paper should have said so in one sentence. Second, and less discussed: Sec. 7.4 honestly flags that the NNLO trap integral diverges at the cloud edge, and the boundary layer contributes an error of order N^{5/9}, only N^{-1/9} below the NLO term. That is a real ceiling on the trap-energy prediction, and they deserve credit for stating it. The conformal-exactness argument via tuneable q0, r0 is clever but heuristic; fine as far as it goes. Citations are clean and appropriately placed. This is for cold-atom theorists, EFT people, and anyone working the unitary gas. Send it to a serious referee.

Referee report

Significance

If the result holds, this is a valuable and durable contribution: it identifies a symmetry that is invisible in flat space but constrains the flat-space EFT, and it reduces the low-momentum dynamics of the strongly interacting Fermi gas to three numbers with falsifiable relations among observables (Eq. 8, Eq. 9) that hold for any values of c1 and c2. The paper is explicit and checkable at the points that matter: the cancellation of the ξ-dot terms in Eq. 17 is straightforward to verify, the conformal reduction c3 = -9c2 is carried out step by step in Eqs. 108-114, and the field-equation reduction of the relativistic basis in Eqs. 87-91 is standard. The prediction that c2 > 0 from the sign of the transverse response function (Sec. 7.3) is a genuine, testable statement. No constants are fitted to data and then presented as predictions.

Major objections (3)

[Sec. 6.2, Eqs. 91-102] The completeness of the NLO operator basis is the load-bearing step for the 'two additional constants' claim, and it is asserted rather than proved. The paper classifies relativistic invariants (Eq. 91, four independent functions F1-F4) and takes their nonrelativistic limit to obtain Eqs. 98-102, but does not show the converse: that every nonrelativistic GCI scalar at O(p^2) is the nonrelativistic limit of a relativistic invariant. Since the relativistic diffeomorphism group (Eq. 25) is larger than the nonrelativistic GCI group (Eq. 17), relativistic invariants are automatically GCI invariants, but the converse does not follow automatically, and a GCI term with no relativistic ancestor would add a third constant and break the central claim. The authors should either supply an argument for the converse or state the completeness assumption explicitly as a hypothesis of the construction. This is a rigor gap rather than a demonstrated error: the obvious candidate, (∇²X)f(X), is not independent, since integrating by parts gives -g^{ij}∂_iX∂_jX f'(X), which is the L1 structure of Eq. 99.
[Sec. 6.2, Eq. 103 and Eq. 106] The comparison with Galilean invariance is a useful check but is presented too briefly to be convincing. The text states that the third expression in Eq. 106 does not enter the Lagrangian at all and that the first two enter only through one linear combination, so that Galilean invariance alone would give five arbitrary functions instead of three. The reader is asked to take this on trust; a short explicit demonstration (or an appendix) showing how the five Galilean-invariant structures collapse to the three GCI structures of Eq. 103 would make the central 'GCI is more restrictive than Galilean invariance' point verifiable rather than asserted.
[Sec. 7.4, Eqs. 142-147] The boundary-layer discussion is honest and useful, but its consequence for the claimed predictive power should be stated more sharply in the main text. The estimate F_boundary ~ µ^{5/3}ω^{2/3} translates into an uncertainty of order N^{5/9} in Eq. 141, which is only a factor N^{-1/9} smaller than the NLO correction the paper is trying to isolate. This means that for realistic trapped samples the NLO coefficient combination (c1 - 9c2/2) extracted from trap energies may be numerically entangled with the boundary-layer uncertainty. The authors should quantify this for typical N values and state clearly which observables (e.g. the homogeneous response functions of Secs. 7.2-7.3) are free of this limitation.

Minor objections (6)

[Sec. 2, Eq. 4] The NLO Lagrangian in Eq. 4 is written with a term -9m∇²A0 inside the bracket multiplying c2, but the corresponding flat-space expression in Eq. 116 uses -9m∇²A0 with a different sign convention for A0 relative to X; the two should be checked for consistency, since a reader comparing the summary with the derivation will be confused.
[Sec. 3.1, Eq. 16] The statement that the action acquires a change proportional to ξ-dot (Eq. 16) is correct, but the text would be clearer if it noted explicitly that the symmetric form of the time-derivative term is what makes the cancellation in Eq. 17 possible, rather than leaving this remark to the parenthetical after Eq. 17.
[Sec. 4, footnote 2] The remark that the literature uses 'conformal transformation' for a particular combination of Eq. 38 and Eq. 17 is helpful, but the paper should state once, in the main text, which convention it adopts throughout, since the term is used in both senses in the subsequent sections.
[Sec. 5.3, Eq. 63] The derivation of the leading-order Lagrangian as a function of X is clean, but the paper should note explicitly that the identification of P with the pressure (Eq. 64 and following) fixes the normalization of X, since a shift in X can be absorbed into a redefinition of the chemical potential.
[Sec. 7.1, Eq. 120] The statement that the dispersion curves up and a low-energy phonon can decay into two phonons when 2c1 + 3c2 < 0 should be accompanied by a brief kinematic argument or a reference, since the sign of the q^3 correction alone does not by itself establish the decay channel.
[References] The paper cites Refs. [16, 17] for the alternative use of 'conformal transformation' but does not cite the subsequent effective-field-theory literature on the unitary Fermi gas at NLO; a brief note on how the present counting compares with that work would help the reader place the result.

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The paper

The paper claims

Nonrelativistic physics has a hidden general-coordinate symmetry, and it pins the unitary Fermi gas to three numbers.

The reading

The paper asks how much of the physics of a strongly interacting, nonrelativistic gas is fixed by symmetry alone. Its authors show that the Lagrangian of nonrelativistic particles can be coupled to an external gauge field and a curved spatial metric in a way that is invariant under a nonrelativistic version of general coordinate transformations, a gauging of translations and Galilean boosts that also enforces conservation of particle number and momentum. Applied to the unitary Fermi gas, where the two-body scattering length is infinite and conformal invariance becomes exact, this symmetry plus a momentum expansion leaves only one constant at leading order (the same $c_0$, equivalently $xi$, that Thomas-Fermi theory and superfluid hydrodynamics already need) and only two more, $c_1$ and $c_2$, at next-to-leading order. Because those three numbers are fewer than the number of quantities the theory predicts, the effective theory has real predictive power: it relates the $q^3$ correction to the phonon dispersion, the $q^2$ corrections to the static density and transverse response functions, and the leading correction to the trapped-gas energy. A reader should care because this turns an intractable strongly coupled problem into a short list of measurable coefficients plus exact relations among observables.

What carries the argument

The load-bearing object is the invariant combination $X = D_t theta - g^{ij} D_i theta D_j theta /(2m)$, built from the gauge-covariant time and space derivatives of the condensate phase. Under general coordinate transformations $X$ transforms as a scalar, so the leading-order Lagrangian must be a function $P(X)$ of it alone; evaluating $P$ at the ground state $theta = mu t$ identifies it with the thermodynamic pressure, which is how Thomas-Fermi theory and superfluid hydrodynamics drop out as special cases. At next-to-leading order the machinery is a relativistic lift: the authors classify the seven relativistic order-$p^2$ scalars built from $nabla_mu partial_nu Theta$, the Ricci tensor and the Ricci scalar, use the field equation and integration by parts to reduce them to four, and take the $c to infinity$ limit to obtain the nonrelativistic basis. Conformal invariance, applied as a reparametrization of time with $delta theta = -beta dot{theta}$, then removes one linear combination because the two terms containing time derivatives of the metric fail to have a definite conformal dimension separately but cancel in the ratio $c_3 = -9 c_2$.

Extended reading notes

Core claim

The authors establish that a nonrelativistic many-body Lagrangian can be coupled to an external $A_0$, $A_i$ and a time-dependent spatial metric $g_{ij}$ so that the action is invariant under a deformed coordinate transformation in which a time-dependent spatial shift $xi^k(t)$ is compensated by a shift of the vector potential proportional to $m g_{ik} dot{xi}^k$. This is a gauge version of translations and Galilean boosts, and it implies that the number current equals the momentum density (up to a factor of $m$) in flat space with $A_i = 0$. Combined with the conformal invariance that becomes exact at infinite scattering length, this fixes the effective Lagrangian of the unitary Fermi gas: at leading order $L = c_0 m^{3/2} X^{5/2}$ with $X = D_t theta - g^{ij}D_i theta D_j theta/(2m)$, and at next-to-leading order only two further dimensionless constants survive, $c_1$ and $c_2$, after conformal invariance imposes $c_3 = -9 c_2$ on the three constants that general coordinate invariance alone would allow. The paper then computes physical consequences: the phonon dispersion with its $q^3$ term, the static density and transverse response functions, a relation tying the dispersion correction to those response functions, and the ground-state energy of a trapped gas through order $N^{2/3}$.

Load-bearing premise

The claim that only two new constants appear at next-to-leading order rests on the assumption that every nonrelativistic term consistent with general coordinate invariance can be reached by taking the nonrelativistic limit of a relativistic term, which the paper asserts rather than proves.

Editorial extensions

If this is right

Every low-momentum observable of the unitary Fermi gas is determined by three numbers, $c_0$ (equivalently $xi$), $c_1$ and $c_2$, so measuring any three independent quantities fixes the rest.
The nonlinear $q^3$ term in the phonon dispersion and the $q^2$ corrections to the static density and transverse response functions are tied together by a parameter-free relation, Eq. (8), which can be checked without knowing $c_1$ or $c_2$.
The trapped-gas energy acquires a calculable $N^{2/3}$ correction proportional to $(c_1 - tfrac{9}{2} c_2)(omega_1^2 + omega_2^2 + omega_3^2)/bar{omega}$, giving a second, independent handle on the same combination of constants.
The sign of $c_2$ is fixed to be positive by the requirement that the static transverse response function be negative, so the transverse response provides a consistency check rather than a free fit.
At finite scattering length the conformal symmetry is broken explicitly by a term proportional to $1/a$ with its own coefficient, giving a controlled way to interpolate away from the unitary limit.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

If the three-constant description holds, the natural next step is a lattice or quantum Monte Carlo extraction of $c_1$ and $c_2$ from the small-$q$ density and transverse response functions, which would turn the relation in Eq. (8) into a genuine numerical test rather than a consistency condition.
The same general-coordinate construction should apply to any nonrelativistic superfluid with a known equation of state, so the framework suggests a systematic route to next-to-leading-order hydrodynamics for cold Bose gases and for mixtures, where the paper itself sketches a two-gauge-field extension for a $^4$He-$^3$He-like system.
The boundary-layer problem noted near the edge of a trapped cloud is a structural warning: higher-order terms in the derivative expansion diverge there, so any precision test of the next-to-leading-order coefficients is best done in a uniform gas rather than in a trap.
Because the operator basis is obtained by lifting relativistic invariants and then taking $c to infinity$, a purely nonrelativistic invariant with no relativistic ancestor would be an extra, unconstrained term; searching for such a term is the sharpest way to test whether the counting of constants is complete.

Original abstract

We show that the Lagrangian for interacting nonrelativistic particles can be coupled to an external gauge field and metric tensor in a way that exhibits a nonrelativistic version of general coordinate invariance. We explore the consequences of this invariance on the example of the degenerate Fermi gas at infinite scattering length, where conformal invariance also plays an important role. We find the most general effective Lagrangian consistent with both general coordinate and conformal invariance to leading and next-to-leading orders in the momentum expansion. At the leading order the Lagrangian contains one phenomenological constant and reproduces the results of the Thomas-Fermi theory and superfluid hydrodynamics. At the next-to-leading order there are two additional constants. We express various physical quantities through these constants.

The compiled record

The paper's own sentences, arranged, kept beside the review and separate from it. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.

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What the abstract itself states, as probabilities: claims first 0.04 · states limitation 0.19 · human participants 0.01 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.49 · compares with prior results 0.68 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v2. Results and the main claim are underlined; show every role.

We show that the Lagrangian for interacting nonrelativistic particles can be coupled to an external gauge field and metric tensor in a way that exhibits a nonrelativistic version of general coordinate invariance. We explore the consequences of this invariance on the example of the degenerate Fermi gas at infinite scattering length, where conformal invariance also plays an important role. We find the most general effective Lagrangian consistent with both general coordinate and conformal invariance to leading and next-to-leading orders in the momentum expansion. At the leading order the Lagrangian contains one phenomenological constant and reproduces the results of the Thomas-Fermi theory and superfluid hydrodynamics. At the next-to-leading order there are two additional constants. We express various physical quantities through these constants.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#	sentence	role	the authors' own work	states the main conclusion	strength
s0	We show that the Lagrangian for interacting nonrelativistic particles can be coupled to an external gauge field and metric tensor in a way that exhibits a nonrelativistic version of general coordinate invariance.	contribution 0.89	0.94	0.54	asserted 1.00
s1	We explore the consequences of this invariance on the example of the degenerate Fermi gas at infinite scattering length, where conformal invariance also plays an important role.	contribution 0.80	0.85	0.07	asserted 0.92
s2	We find the most general effective Lagrangian consistent with both general coordinate and conformal invariance to leading and next-to-leading orders in the momentum expansion.	contribution 0.65	0.96	0.36	asserted 1.00
s3	At the leading order the Lagrangian contains one phenomenological constant and reproduces the results of the Thomas-Fermi theory and superfluid hydrodynamics.	result 0.99	0.84	0.18	asserted 1.00
s4	At the next-to-leading order there are two additional constants.	result 0.98	0.86	0.07	asserted 1.00
s5	We express various physical quantities through these constants.	contribution 0.53	0.92	0.12	asserted 0.99

What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from proof or derivation 1.00.

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sources read

arXiv listing abstract v2

not examined

full text
figures and tables
references and citing sentences
relations to other papers

levels run

P abstract

not run

S sections
T body sentences
C citations
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Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

Figures

**Figure 1.** A one loop contribution to the phonon self-energy.

**Figure 2.** A one loop contribution to the phonon scattering am

Figures reproduced from arXiv:cond-mat/0509786 by the authors.

References

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hep-lat 2017-07 conditional novelty 6.0 of 10

Monte Carlo measurements at the O(2) Wilson-Fisher fixed point confirm that conformal dimensions of charge-Q operators follow a 1/Q expansion whose first three terms already fit the data.
Three-Dimensional Extended Bargmann Supergravity
hep-th 2016-04 conditional novelty 6.0 of 10

A non-relativistic limit of three-dimensional gravity with two vector fields produces a Chern-Simons 'Extended Bargmann Gravity' that admits spatially curved matter backgrounds, and the authors construct its supersymm...
Newton-Cartan (super)gravity as a non-relativistic limit
hep-th 2015-05 accept novelty 6.0 of 10

A systematic non-relativistic limit of relativistic supergravity produces a new off-shell three-dimensional Newton-Cartan supergravity multiplet with a single auxiliary scalar.
Curved non-relativistic spacetimes, Newtonian gravitation and massive matter
hep-th 2015-03 accept novelty 6.0 of 10

A general Bargmann spacetime is built from an extended coframe, with a mass gauge field and torsion, and shown to contain Newton-Cartan geometry and Newtonian gravity as special cases.
Fields and fluids on curved non-relativistic spacetimes
hep-th 2015-03 conditional novelty 6.0 of 10

Keeping an independent boost connection in Newton-Cartan geometry changes the allowed first-order transport coefficients of non-relativistic fluids, adding new parity-even and parity-odd terms for multicomponent systems.
Revisiting non-relativistic limits
hep-th 2014-12 conditional novelty 6.0 of 10

Newton-Cartan geometry and Milne boosts, the spurionic symmetries of Galilean field theories, are derived as the c to infinity limit of a relativistic parent with a chemical potential equal to the rest mass.
On the coupling of Galilean-invariant field theories to curved spacetime
hep-th 2014-08 accept novelty 6.0 of 10

Galilean-invariant field theories couple to Newton-Cartan geometry plus a Milne shift symmetry, and that same structure arises automatically from null reduction of a Lorentzian manifold in one higher dimension.
Spacetime Symmetries of the Quantum Hall Effect
cond-mat.mes-hall 2014-07 accept novelty 6.0 of 10

The paper derives spacetime-covariant Ward identities for non-relativistic quantum Hall systems using Newton-Cartan geometry with torsion, and reproduces the known relation between Hall viscosity and Hall conductivity.
Dark Matter Thermalization in Neutron Stars
hep-ph 2013-09 conditional novelty 6.0 of 10

Including Pauli blocking, kinematic constraints, and superfluid or superconducting gaps lengthens dark matter thermalization times in neutron stars, in some phases by many orders of magnitude, weakening existing dark ...
Non-relativistic holography from Horava gravity
hep-th 2012-10 conditional novelty 6.0 of 10

Horava gravity coupled to non-relativistic electromagnetic fields is proposed as the holographic dual of any non-relativistic field theory with time-dependent spatial diffeomorphisms and a conserved particle number.
On Representations and Correlation Functions of Galilean Conformal Algebras
hep-th 2009-03 conditional novelty 6.0 of 10

The two- and three-point functions of quasi-primary operators in the Galilean Conformal Algebra are fixed by the finite subalgebra up to constants, with a rapidity quantum number producing an exponential spatial depen...
An obstruction to cosmic acceleration from shift-symmetric dark sector interactions
astro-ph.CO 2026-11 accept novelty 5.0 of 10

Derivative interactions in the dark sector between a perfect fluid and a superfluid cannot stably sustain slow-roll expansion and prevent phantom-to-non-phantom crossing.
Aspects of Galileon Non-Renormalization
hep-th 2016-06 conditional novelty 5.0 of 10

Galileon interaction operators are not renormalized by loops of heavy fields coupled in a symmetry-respecting way, unlike the leading operators of general relativity, P(X) theories, and the conformal dilaton, which are.
Ultralight Repulsive Dark Matter and BEC
hep-ph 2016-03 conditional novelty 5.0 of 10

A repulsive self-interaction for ultralight axion dark matter is possible if the axion is the Wilson loop of a 5D gauged U(1) with 5D matter charges tuned to satisfy two inequalities.
Connections and dynamical trajectories in generalised Newton-Cartan gravity I. An intrinsic view
hep-th 2014-12 accept novelty 5.0 of 10

The space of torsional Galilean connections is an affine space modelled on 2-forms plus spacelike torsion, and torsional Newtonian connections are those whose gravitational fieldstrength is covariantly exact.
Effective Field Theories for Material Media
hep-th 2026-07 accept novelty 4.0 of 10

Spacetime-symmetry-breaking Goldstone EFTs systematically describe bulk and localized excitations of solids, fluids, and superfluids, with new thermodynamic identifications and corrected scattering rates.
Observables in Schr\"odinger CFTs: How Aliens Built the Pyramids
hep-th 2026-06 unverdicted novelty 4.0 of 10

Observables in Schrödinger CFTs have zero mass and transform in staggered pyramid representations built from alien operators, generalizing exceptional symmetry conservation laws.
Emergent Hall viscosity in the integer quantum Hall phases of graphene-like systems
cond-mat.mes-hall 2026-06 unverdicted novelty 4.0 of 10

Emergent Hall viscosity for integer quantum Hall phases in graphene is derived as a sum of geometric and electronic terms that depends on two topological invariants obtained via Green function Wigner-Weyl calculus.
Universalities of Defects in Quantum Field Theories
hep-th 2026-05 unverdicted novelty 4.0 of 10

A dissertation synthesizing universal aspects of defect dynamics in QFT through symmetry principles across defect RG flows, effective strings, and quantum gas impurities.
Spontaneous Symmetry Breaking and Nambu-Goldstone Bosons in Quantum Many-Body Systems
hep-th 2010-01 accept novelty 4.0 of 10

In systems without Lorentz invariance the number of Nambu-Goldstone bosons need not equal the number of broken generators, and the shortfall is governed by dispersion type and by ground-state charge densities.
Reaction rates and transport in neutron stars
astro-ph.HE 2017-11 accept novelty 2.0 of 10

The review compiles and organizes the transport coefficients and weak-interaction reaction rates of neutron star matter from crust to quark core, and identifies where the underlying nuclear and QCD physics remains uncertain.
Nearly Perfect Fluidity: From Cold Atomic Gases to Hot Quark Gluon Plasmas
hep-ph 2009-04 accept novelty 2.0 of 10

Superfluid helium, ultracold Fermi gases, and the quark-gluon plasma all reach a shear viscosity to entropy ratio within a factor of a few of the conjectured quantum bound 1/(4 pi).

How later papers used it

135 later papers cite it

Evidence: substantial. 132 of the citing papers share no author with it, and 17 of those carry a confident label from Pith's citation classifier.

Pith read 19 of the 316 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

3 later papers by other authors are listed below: 1 built on it and 2 used its method or tool.

Builds on it 1 of 5 papers with this label

We then went on to build the complete large-charge eft, to be regarded as the extension of the Son & Wingate eft [ref] .

The large-charge expansion in nonrelativistic conformal field theories (2025) · Closing word · 1.00

Uses its method or tool 2 of 6 papers with this label

Based its procedure on an effective Lagrangian for the Fermi gas in the unitarity limit derived in this paper.

Density Functional Theory for non-relativistic Fermions in the Unitarity Limit (2008) · 0.83 · paraphrased: the licence does not allow quoting
Used the scattering rates obtained from this paper's EFT Lagrangian to evaluate η via Beliaev 1↔2 processes.

Phonon contribution to the shear viscosity of a superfluid Fermi gas in the unitarity limit (2012) · 0.84 · paraphrased: the licence does not allow quoting

How the literature uses it

100 arXiv papers cite this in 236 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 · 175 sentences without a confident label

Contests it 1 paper

However, non-relativistic spacetimes can not have a preferred vector field and so we must have invariance under a change of choice of $v^μ$, the so called Milne boosts v^μ↦v^μ+ k^μ where k^μn_μ= 0 In [ref] , Milne boosts were conflated with certain time-dependent spatial diffeomorphisms acting on tensors fields on $M$, and the tensor fields were assigned anomalous transformation properties under diffeomorphisms to maintain certain invariance properties.

Curved non-relativistic spacetimes, Newtonian gravitation and massive matter · Introduction · contest 0.82

Builds on it 4 papers

We then went on to build the complete large-charge eft, to be regarded as the extension of the Son & Wingate eft [ref] .

The large-charge expansion in nonrelativistic conformal field theories · Closing word · 1.00
While a complete description of the crossover is still lacking, the emergent scale invariance at unitarity allows for an eft description of the cold Fermi gas with a large number of trapped particles, as initiated by Son & Wingate [ref] and completed in the present work from a lsm perspective, where the only massless, low-energy degree of freedom $χ$ corresponds to the phase of the condensate.

Operator spectrum of nonrelativistic CFTs at large charge · Introduction · 0.88
This generalizes the action found in Ref. [ref] to an arbitrary spacetime background, including sources for momentum density and energy density and current.

General coordinate invariance in quantum many-body systems · Superfluid effective theory · 0.99

Uses its method or tool 3 papers

Our procedure is based on an effective lagrangian for the Fermi gas in the unitarity limit derived in [ref] .

Density Functional Theory for non-relativistic Fermions in the Unitarity Limit · Introduction · 0.83
For the evaluation of $η$, we consider the Beliaev $1 ↔2$ processes, using for this purpose the scattering rates obtained from the EFT Lagrangian of Ref. [ref] .

Phonon contribution to the shear viscosity of a superfluid Fermi gas in the unitarity limit · Introduction · 0.84
We here employ the effective field theory based on the symmetries and the systematic derivative expansion following Refs. [ref] .

Hall viscosity in the A-phase of superfluid $^3$He · Introduction · 0.99

Compares with it 4 papers

It will turn out that the sharp conformal cutoff is equivalent to the “cloud radius" cutoff used in [ref] , but organized in a more manifestly conformal way.

Droplet-Edge Operators in Nonrelativistic Conformal Field Theories · Conformal sharp cutoff in $d=2$ · 0.80
The opposite sign in front of the $g^μν/2mD_μπD_νπ$ term as compared to Ref. [ref] is just a matter of a sign convention for the field $π$.] [equation] where $P$ defines the thermodynamic pressure of the system at zero temperature as a function of the chemical potential for the U(1) symmetry.

General coordinate invariance in quantum many-body systems · Superfluid effective theory · 0.93
This is consistent with the analysis in [ref] .

Spontaneous Breaking of Non-Relativistic Scale Symmetry · Spectrum Analysis · 0.89

Cites it as support 1 paper

As argued in [ref] , the transverse response should be positive to ensure stability with respect to a spontaneous generation of currents or formation of inhomogeneous condensates.

Validating Simple Dynamical Simulations of the Unitary Fermi Gas · Linear Response · 0.98

Cites it as background 41 papers

At low-energies, the UFG can be characterized by a superfluid EFT describing phonon dynamics [ref] .

The Unitary Fermi Gas in a Harmonic Trap and its Static Response · Introduction · 0.81
The constraints imposed by Galilean invariance and conformal symmetry on the structure of the Navier-Stokes equation were studied by Son [ref] based on earlier work by Son and Wingate [ref] .

Conformal symmetry and non-relativistic second order fluid dynamics · Navier-Stokes equation · 0.92
In Sec. [ref] we review the phonon EFT at leading order and next-to-leading order in a derivative expansion [ref] .

Effective field theory and dispersion law of the phonons of a non-relativistic superfluid · Introduction · 0.96

Discussion

Disagree with the review, or know something it missed? Leave a comment, highlight any passage above to comment on it, or challenge this review formally.

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