Non-relativistic effective theories for fields with general potentials and their implications for cosmology

H.S. Modirzadeh; M.H. Namjoo; R. Moti

arxiv: 2507.08786 · v2 · submitted 2025-07-11 · 🌌 astro-ph.CO · gr-qc· hep-ph· hep-th

Non-relativistic effective theories for fields with general potentials and their implications for cosmology

H.S. Modirzadeh , R. Moti , M.H. Namjoo This is my paper

Pith reviewed 2026-05-19 04:59 UTC · model grok-4.3

classification 🌌 astro-ph.CO gr-qchep-phhep-th

keywords non-relativistic effective field theorygeneric potentialsscalar field cosmologyultra-light dark mattereffective fluid descriptionsolitonsexpanding universenon-analytic potentials

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The pith

A systematic framework derives non-relativistic effective field theories from relativistic scalar theories with arbitrary self-interaction potentials.

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

The paper develops a general method to obtain non-relativistic effective field theories from relativistic scalar field models that include any form of self-interaction potential. This covers cases beyond simple power laws, such as potentials from dilatons or axions, and non-analytic forms with logarithmic corrections. The construction keeps the non-relativistic limit valid by requiring only that the mass term dominates, without needing small field amplitudes. From there the authors derive an effective fluid picture with explicit energy density, pressure and sound speed, then adapt the whole setup to an expanding universe. The result supplies a practical tool for ultra-light dark matter models with complex interactions and for analyzing solitons that appear in boson stars or dark matter halo cores.

Core claim

We present a systematic framework for deriving NREFTs from relativistic theories with generic self-interactions. Our approach allows for non-power-law potentials such as those arising from dilatons or axions or potentials that are non-analytic around the classical vacuum such as those with logarithmic radiative corrections. The non-relativistic limit remains valid as long as the mass term remains dominant even when relaxing the small field amplitude assumption. We establish an effective fluid description for the non-relativistic scalar field and extend the formalism to the expanding universe to investigate ultra-light dark matter models with arbitrary self-interactions, demonstrating its use

What carries the argument

The systematic derivation that maps a relativistic action with generic potentials to the non-relativistic effective field theory while producing associated fluid variables such as energy density, pressure and sound speed.

Load-bearing premise

The non-relativistic limit remains valid as long as the mass term remains dominant, even when the small field amplitude assumption is relaxed.

What would settle it

A side-by-side comparison of full relativistic numerical simulations against the NREFT fluid equations for a specific non-analytic potential, such as one containing logarithmic terms, would show whether soliton profiles or cosmological evolution match or deviate.

Figures

Figures reproduced from arXiv: 2507.08786 by H.S. Modirzadeh, M.H. Namjoo, R. Moti.

**Figure 2.** Figure 2: Soliton’s profile for a quadratic potential, altered by a logarithmic factor. The blue curve [PITH_FULL_IMAGE:figures/full_fig_p020_2.png] view at source ↗

**Figure 3.** Figure 3: Soliton’s profile for V0( |ψs| ψ0 ) 4 with and without the logarithmic factor. For these plots we have set m, ψ0 and |V0| the same as those in [PITH_FULL_IMAGE:figures/full_fig_p020_3.png] view at source ↗

read the original abstract

Non-relativistic effective field theories (NREFTs) play a crucial role in various areas of physics, from cold atom experiments to cosmology. In this paper, we present a systematic framework for deriving NREFTs from relativistic theories with generic self-interactions. Our approach allows for (but is not limited to) non-power-law potentials (such as those arising from dilatons or axions) or potentials that are non-analytic around the classical vacuum (such as those with logarithmic radiative corrections). These are of theoretical and phenomenological interest but have largely been unexplored in the non-relativistic regime. NREFTs are typically viewed as approximations for systems with low velocities, weak couplings, and small field amplitudes. The latter assumption is relaxed in our approach, as long as the mass term remains dominant (ensuring the validity of the non-relativistic limit). Additionally, we establish an effective fluid description for the non-relativistic scalar field, identifying key quantities such as energy density, pressure, and sound speed. To enable cosmological applications, we extend our formalism to account for the expanding universe, providing a reliable tool for investigating ultra-light dark matter models with arbitrary self-interactions. Finally, we demonstrate the applicability of our NREFT in analyzing solitons, which is also relevant to cosmology for studying celestial objects such as boson stars and the cores of dark matter halos.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

The paper gives a systematic NREFT derivation for general potentials including non-analytic ones, but the mass-dominance assumption for large amplitudes lacks explicit bounds.

read the letter

The main takeaway is that this work lays out a general procedure to derive non-relativistic effective theories from relativistic scalars with arbitrary self-interaction potentials, then builds a fluid description and extends it to cosmology for ultra-light dark matter. They relax the usual small-amplitude restriction provided the mass term stays dominant, which lets them treat non-power-law cases like dilatons or axions and non-analytic forms with logarithmic corrections. The soliton section applies the setup to boson stars and dark matter halo cores, which is a concrete step toward structure-formation studies. What stands out is the move away from case-by-case treatments toward a single framework that covers potentials previously left aside in the non-relativistic regime. The fluid quantities and expanding-universe adaptation follow logically from the effective Lagrangian once the limit is taken. The soft spot is the central premise that the non-relativistic hierarchy continues to hold at larger field amplitudes for these general potentials. Non-analytic terms can generate effective scales that compete with the mass even when m is the largest explicit parameter, and the abstract plus outline give no error estimates, counter-example checks, or expansion-order analysis to confirm the assumption stays uniform. Without those, the range of validity remains unclear. This is aimed at cosmologists and particle physicists already working on fuzzy dark matter or light scalars who want to explore less standard potentials. A reader familiar with standard power-law NREFTs will see the generalization most clearly. The methodological advance and cosmological relevance are enough to justify sending it to a serious referee, though the assumption on large-amplitude validity will probably need tightening or explicit verification in revision.

Referee Report

1 major / 1 minor

Summary. The paper presents a systematic framework for deriving non-relativistic effective field theories (NREFTs) from relativistic scalar field theories with generic self-interaction potentials, including non-power-law forms (e.g., dilatons or axions) and non-analytic potentials (e.g., with logarithmic radiative corrections). It relaxes the usual small-amplitude assumption provided the mass term remains dominant, derives an effective fluid description identifying energy density, pressure, and sound speed, extends the formalism to an expanding universe for cosmological applications such as ultra-light dark matter, and demonstrates applicability to solitons relevant to boson stars and dark matter halo cores.

Significance. If the central claims hold, the work would provide a useful extension of NREFT techniques to a broader class of potentials relevant for ultra-light dark matter models in cosmology. The ability to handle non-analytic potentials without restricting to small amplitudes or power-law forms could enable more realistic modeling of self-interactions arising from radiative corrections or specific high-energy completions, with the fluid description and expanding-universe extension offering practical tools for analyzing structure formation and solitonic configurations.

major comments (1)

[Abstract and derivation of the NREFT] The central premise that the non-relativistic limit and fluid description remain valid for generic (including non-analytic) potentials as long as the mass term dominates, even after relaxing the small field amplitude assumption, lacks explicit error bounds or counter-example verification. For potentials with logarithmic or other non-analytic corrections, the expansion around the vacuum can generate effective interaction scales that compete with the mass term at moderate amplitudes, potentially violating the NR hierarchy; this assumption underpins both the effective Lagrangian construction and the cosmological fluid equations and requires quantitative support.

minor comments (1)

[Fluid description section] Clarify the precise regime of validity for the fluid quantities (energy density, pressure, sound speed) when the potential is non-analytic, including any additional assumptions beyond mass-term dominance.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for their careful reading and constructive comments on our manuscript. We address the major comment below and have revised the manuscript to provide additional quantitative support for the validity of the non-relativistic limit.

read point-by-point responses

Referee: [Abstract and derivation of the NREFT] The central premise that the non-relativistic limit and fluid description remain valid for generic (including non-analytic) potentials as long as the mass term dominates, even after relaxing the small field amplitude assumption, lacks explicit error bounds or counter-example verification. For potentials with logarithmic or other non-analytic corrections, the expansion around the vacuum can generate effective interaction scales that compete with the mass term at moderate amplitudes, potentially violating the NR hierarchy; this assumption underpins both the effective Lagrangian construction and the cosmological fluid equations and requires quantitative support.

Authors: We appreciate the referee pointing out the need for more explicit justification of the validity regime. Our derivation obtains the NREFT by substituting the standard non-relativistic ansatz into the relativistic action and averaging over rapid oscillations, with the key assumption being that the mass term sets the dominant frequency scale so that corrections from the potential remain perturbative. For non-analytic potentials we expand around the vacuum minimum while retaining the full functional form in the effective theory. We agree that the manuscript would benefit from quantitative error estimates. In the revised version we will add a dedicated paragraph (in the section deriving the NREFT) that provides order-of-magnitude bounds on the neglected terms, showing that the effective frequency shift induced by a logarithmic correction remains ≪ m provided the field amplitude satisfies a simple inequality involving the radiative coefficient. We will also briefly illustrate the hierarchy with a concrete logarithmic example and confirm that the same bound propagates to the fluid variables and the cosmological equations. These additions supply the requested quantitative support while leaving the central formalism unchanged. revision: yes

Circularity Check

0 steps flagged

Derivation of NREFT for generic potentials is self-contained from relativistic starting point

full rationale

The paper derives NREFTs and an effective fluid description directly from relativistic theories with stated generic potentials (including non-power-law and non-analytic cases), relaxing the small-amplitude assumption provided the mass term dominates. This chain begins from the relativistic action and proceeds to the non-relativistic limit and cosmological extensions without any reduction of outputs to fitted parameters, self-definitions, or load-bearing self-citations. No equations or steps are shown to be equivalent to their inputs by construction, and the framework remains independent of the target results.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The framework rests on the dominance of the mass term for validity of the non-relativistic limit and on the existence of relativistic parent theories with generic potentials drawn from prior literature; no new free parameters or invented entities are explicitly introduced in the abstract.

axioms (1)

domain assumption The non-relativistic limit holds when the mass term remains dominant even for non-small field amplitudes.
Invoked to relax the small-amplitude assumption while preserving the effective theory construction.

pith-pipeline@v0.9.0 · 5792 in / 1325 out tokens · 38827 ms · 2026-05-19T04:59:32.654367+00:00 · methodology

discussion (0)

Forward citations

Cited by 1 Pith paper

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Reference graph

Works this paper leans on

24 extracted references · 24 canonical work pages · cited by 1 Pith paper · 10 internal anchors

[1]

Effective Lagrangians for simulating heavy quark systems

G. P. Lepage and B. A. Thacker, “Effective Lagrangians for simulating heavy quark systems”, Nucl. Phys. B 4, 199 (1988). 26

work page 1988
[2]

Effective Field Theory for Ultrasoft Momenta in NRQCD and NRQED

A. Pineda and J. Soto, “Effective field theory for ultrasoft momenta in NRQCD and NRQED”, Nucl. Phys. B 514, 609 (1998) arXiv:hep-ph/9707481 [hep-ph]

work page internal anchor Pith review Pith/arXiv arXiv 1998
[3]

C. J. Pethick and H. Smith, Bose-Einstein condensation in dilute gases (2nd ed.), Cambridge University Press (2008)

work page 2008
[4]

Pitaevskii and S

L. Pitaevskii and S. Stringari, Bose-Einstein condensation and superfluidity , Oxford University Press (2016)

work page 2016
[5]

Off-equilibrium infrared structure of self-interacting scalar fields: Universal scaling, Vortex-antivortex superfluid dynamics and Bose-Einstein condensation

J. Deng, S. Schlichting, R. Venugopalan, and Q. Wang, “Off-equilibrium infrared structure of self-interacting scalar fields: Universal scaling, Vortex-antivortex superfluid dynamics and Bose- Einstein condensation”, Phys. Rev. A 97, 053606 (2018) arXiv:1801.06260 [hep-th]

work page internal anchor Pith review Pith/arXiv arXiv 2018
[6]

Do Dark Matter Axions Form a Condensate with Long-Range Correlation?

A. H. Guth, M. P. Hertzberg, and C. Prescod-Weinstein, “Do dark matter axions form a con- densate with long-range correlation?”, Phys. Rev. D 92, 103513 (2015) arXiv:1412.5930 [astro- ph.CO]

work page internal anchor Pith review Pith/arXiv arXiv 2015
[7]

Relativistic Corrections to Nonrelativistic Effective Field Theories

M. H. Namjoo, A. H. Guth, and D.I.Kaiser, “Relativistic corrections to nonrelativistic effective field theories”, Phys. Rev. D 98, 016011 (2018) arXiv:1712.00445 [hep-ph]

work page internal anchor Pith review Pith/arXiv arXiv 2018
[8]

Classical Nonrelativistic Effective Field Theories for a Real Scalar Field

E. Braaten, A. Mohapatra, and H. Zhang, “Classical nonrelativistic effective field theories for a real scalar field”, Phys. Rev. D 98, 096012 (2018) arXiv:1806.01898 [hep-ph]

work page internal anchor Pith review Pith/arXiv arXiv 2018
[9]

On Longevity of I-ball/Oscillon

K. Mukaida, M. Takimoto, and M. Yamada, “On longevity of I-ball/Oscillon”, JHEP 03, 122 (2017) arXiv:1612.07750 [hep-ph]

work page internal anchor Pith review Pith/arXiv arXiv 2017
[10]

Weinberg, Cosmology, Oxford University Press (2008)

S. Weinberg, Cosmology, Oxford University Press (2008)

work page 2008
[11]

Mukhanov, Physical Foundations of Cosmology , Cambridge University Press (2005)

V. Mukhanov, Physical Foundations of Cosmology , Cambridge University Press (2005)

work page 2005
[12]

Salehian, M.H

B. Salehian, M. H. Namjoo, and D. I. Kaiser, “Effective theories for a nonrelativistic field in an expanding universe: Induced self-interaction, pressure, sound speed, and viscosity”, JHEP 07, 059 (2020) arXiv:2005.05388 [astro-ph.CO]

work page arXiv 2020
[13]

Radiative corrections as the origin of spontaneous symmetry breaking

S. Coleman and E. Weinberg, “Radiative corrections as the origin of spontaneous symmetry breaking”, Phys. Rev. D 7, 1888 (1973)

work page 1973
[14]

Pinning down the mechanism of neutrinoless double beta decay with measurements in different nuclei

K. A. Meissner and H. Nicolai, “Conformal symmetry and the standard model”, Phys. Lett. B 648, 312 (2007) arXiv:hep-ph/0612165 [hep-th]. 27

work page internal anchor Pith review Pith/arXiv arXiv 2007
[15]

The dilaton and chiral symmetry breaking

W. A. Bardeen, C. N Leung, and S. T. Love, “The dilaton and chiral symmetry breaking”, Phys. Rev. Lett. 56, 1230 (1986)

work page 1986
[16]

Gasperini, Elements of String Cosmology , Cambridge University Press (2007)

M. Gasperini, Elements of String Cosmology , Cambridge University Press (2007)

work page 2007
[17]

Kuster, G

M. Kuster, G. Raffelt, and B. Beltr´ an, Axions: Theory, Cosmology, and Experimental Searches (Lecture Notes in Physics, 741), Springer (2008)

work page 2008
[18]

Axion as a Cold Dark Matter candidate

J. c. Hwang and H. Noh, “Axion as a cold dark matter candidate”, Phys. Lett. B 680, 1 (2009) arXiv:0902.4738 [astro-ph.CO]

work page internal anchor Pith review Pith/arXiv arXiv 2009
[19]

Dark matter droplets

I.G. Moss, “Dark matter droplets” (2024) arXiv:2407.13243 [astro-ph.CO]

work page arXiv 2024
[20]

Formation of solitons and their transitions in scalar- field dark matter models with a nonpolynomial self-interaction potential

R. Galazo Garc´ ıa, P. Brax and P. Valageas, “Formation of solitons and their transitions in scalar- field dark matter models with a nonpolynomial self-interaction potential”, Phys. Rev. D 111, 063511 (2025) arXiv:2412.02519 [astro-ph.CO]

work page arXiv 2025
[21]

Salehian, H.-Y

B. Salehian, H. Y. Zhang, M. A. Amin, D. I. Kaiser, and M. H. Namjoo, “Beyond Schr¨ odinger- Poisson: nonrelativistic effective field theory for scalar dark matter”, JHEP 09, 050 (2021) arXiv:2104.10128 [astro-ph.CO]

work page arXiv 2021
[22]

Analysis of Dark Matter Axion Clumps with Spherical Symmetry

E. D. Schiappacasse and M. P. Hertzberg, “Analysis of dark matter axion clumps with spherical symmetry”, JCAP 01, 037 (2018) arXiv:1710.04729 [hep-ph]

work page internal anchor Pith review Pith/arXiv arXiv 2018
[23]

Can Light Dark Matter Solve the Core-Cusp Problem?

H. Deng, M. P. Hertzberg, M. H. Namjoo, and A. Masoumi, “Can light dark matter solve the core-cusp problem?”, Phys. Rev. D 98, 023513 (2018) arXiv:1804.05921 [astro-ph.CO]

work page internal anchor Pith review Pith/arXiv arXiv 2018
[24]

A No-Go theorem for the mass-radius relation of solitons

M. H. Namjoo, “A No-Go theorem for the mass-radius relation of solitons”, to appear. 28

work page

[1] [1]

Effective Lagrangians for simulating heavy quark systems

G. P. Lepage and B. A. Thacker, “Effective Lagrangians for simulating heavy quark systems”, Nucl. Phys. B 4, 199 (1988). 26

work page 1988

[2] [2]

Effective Field Theory for Ultrasoft Momenta in NRQCD and NRQED

A. Pineda and J. Soto, “Effective field theory for ultrasoft momenta in NRQCD and NRQED”, Nucl. Phys. B 514, 609 (1998) arXiv:hep-ph/9707481 [hep-ph]

work page internal anchor Pith review Pith/arXiv arXiv 1998

[3] [3]

C. J. Pethick and H. Smith, Bose-Einstein condensation in dilute gases (2nd ed.), Cambridge University Press (2008)

work page 2008

[4] [4]

Pitaevskii and S

L. Pitaevskii and S. Stringari, Bose-Einstein condensation and superfluidity , Oxford University Press (2016)

work page 2016

[5] [5]

Off-equilibrium infrared structure of self-interacting scalar fields: Universal scaling, Vortex-antivortex superfluid dynamics and Bose-Einstein condensation

J. Deng, S. Schlichting, R. Venugopalan, and Q. Wang, “Off-equilibrium infrared structure of self-interacting scalar fields: Universal scaling, Vortex-antivortex superfluid dynamics and Bose- Einstein condensation”, Phys. Rev. A 97, 053606 (2018) arXiv:1801.06260 [hep-th]

work page internal anchor Pith review Pith/arXiv arXiv 2018

[6] [6]

Do Dark Matter Axions Form a Condensate with Long-Range Correlation?

A. H. Guth, M. P. Hertzberg, and C. Prescod-Weinstein, “Do dark matter axions form a con- densate with long-range correlation?”, Phys. Rev. D 92, 103513 (2015) arXiv:1412.5930 [astro- ph.CO]

work page internal anchor Pith review Pith/arXiv arXiv 2015

[7] [7]

Relativistic Corrections to Nonrelativistic Effective Field Theories

M. H. Namjoo, A. H. Guth, and D.I.Kaiser, “Relativistic corrections to nonrelativistic effective field theories”, Phys. Rev. D 98, 016011 (2018) arXiv:1712.00445 [hep-ph]

work page internal anchor Pith review Pith/arXiv arXiv 2018

[8] [8]

Classical Nonrelativistic Effective Field Theories for a Real Scalar Field

E. Braaten, A. Mohapatra, and H. Zhang, “Classical nonrelativistic effective field theories for a real scalar field”, Phys. Rev. D 98, 096012 (2018) arXiv:1806.01898 [hep-ph]

work page internal anchor Pith review Pith/arXiv arXiv 2018

[9] [9]

On Longevity of I-ball/Oscillon

K. Mukaida, M. Takimoto, and M. Yamada, “On longevity of I-ball/Oscillon”, JHEP 03, 122 (2017) arXiv:1612.07750 [hep-ph]

work page internal anchor Pith review Pith/arXiv arXiv 2017

[10] [10]

Weinberg, Cosmology, Oxford University Press (2008)

S. Weinberg, Cosmology, Oxford University Press (2008)

work page 2008

[11] [11]

Mukhanov, Physical Foundations of Cosmology , Cambridge University Press (2005)

V. Mukhanov, Physical Foundations of Cosmology , Cambridge University Press (2005)

work page 2005

[12] [12]

Salehian, M.H

B. Salehian, M. H. Namjoo, and D. I. Kaiser, “Effective theories for a nonrelativistic field in an expanding universe: Induced self-interaction, pressure, sound speed, and viscosity”, JHEP 07, 059 (2020) arXiv:2005.05388 [astro-ph.CO]

work page arXiv 2020

[13] [13]

Radiative corrections as the origin of spontaneous symmetry breaking

S. Coleman and E. Weinberg, “Radiative corrections as the origin of spontaneous symmetry breaking”, Phys. Rev. D 7, 1888 (1973)

work page 1973

[14] [14]

Pinning down the mechanism of neutrinoless double beta decay with measurements in different nuclei

K. A. Meissner and H. Nicolai, “Conformal symmetry and the standard model”, Phys. Lett. B 648, 312 (2007) arXiv:hep-ph/0612165 [hep-th]. 27

work page internal anchor Pith review Pith/arXiv arXiv 2007

[15] [15]

The dilaton and chiral symmetry breaking

W. A. Bardeen, C. N Leung, and S. T. Love, “The dilaton and chiral symmetry breaking”, Phys. Rev. Lett. 56, 1230 (1986)

work page 1986

[16] [16]

Gasperini, Elements of String Cosmology , Cambridge University Press (2007)

M. Gasperini, Elements of String Cosmology , Cambridge University Press (2007)

work page 2007

[17] [17]

Kuster, G

M. Kuster, G. Raffelt, and B. Beltr´ an, Axions: Theory, Cosmology, and Experimental Searches (Lecture Notes in Physics, 741), Springer (2008)

work page 2008

[18] [18]

Axion as a Cold Dark Matter candidate

J. c. Hwang and H. Noh, “Axion as a cold dark matter candidate”, Phys. Lett. B 680, 1 (2009) arXiv:0902.4738 [astro-ph.CO]

work page internal anchor Pith review Pith/arXiv arXiv 2009

[19] [19]

Dark matter droplets

I.G. Moss, “Dark matter droplets” (2024) arXiv:2407.13243 [astro-ph.CO]

work page arXiv 2024

[20] [20]

Formation of solitons and their transitions in scalar- field dark matter models with a nonpolynomial self-interaction potential

R. Galazo Garc´ ıa, P. Brax and P. Valageas, “Formation of solitons and their transitions in scalar- field dark matter models with a nonpolynomial self-interaction potential”, Phys. Rev. D 111, 063511 (2025) arXiv:2412.02519 [astro-ph.CO]

work page arXiv 2025

[21] [21]

Salehian, H.-Y

B. Salehian, H. Y. Zhang, M. A. Amin, D. I. Kaiser, and M. H. Namjoo, “Beyond Schr¨ odinger- Poisson: nonrelativistic effective field theory for scalar dark matter”, JHEP 09, 050 (2021) arXiv:2104.10128 [astro-ph.CO]

work page arXiv 2021

[22] [22]

Analysis of Dark Matter Axion Clumps with Spherical Symmetry

E. D. Schiappacasse and M. P. Hertzberg, “Analysis of dark matter axion clumps with spherical symmetry”, JCAP 01, 037 (2018) arXiv:1710.04729 [hep-ph]

work page internal anchor Pith review Pith/arXiv arXiv 2018

[23] [23]

Can Light Dark Matter Solve the Core-Cusp Problem?

H. Deng, M. P. Hertzberg, M. H. Namjoo, and A. Masoumi, “Can light dark matter solve the core-cusp problem?”, Phys. Rev. D 98, 023513 (2018) arXiv:1804.05921 [astro-ph.CO]

work page internal anchor Pith review Pith/arXiv arXiv 2018

[24] [24]

A No-Go theorem for the mass-radius relation of solitons

M. H. Namjoo, “A No-Go theorem for the mass-radius relation of solitons”, to appear. 28

work page