---
_id: '14542'
abstract:
- lang: eng
  text: "It is a remarkable property of BCS theory that the ratio of the energy gap
    at zero temperature Ξ\r\n and the critical temperature Tc is (approximately) given
    by a universal constant, independent of the microscopic details of the fermionic
    interaction. This universality has rigorously been proven quite recently in three
    spatial dimensions and three different limiting regimes: weak coupling, low density
    and high density. The goal of this short note is to extend the universal behavior
    to lower dimensions d=1,2 and give an exemplary proof in the weak coupling limit."
acknowledgement: We thank Robert Seiringer for comments on the paper. J. H. gratefully
  acknowledges  partial  financial  support  by  the  ERC  Advanced  Grant  “RMTBeyond”No.
  101020331.This research was funded in part by the Austrian Science Fund (FWF) grantnumber
  I6427.
article_number: '2360005 '
article_processing_charge: Yes (in subscription journal)
article_type: original
arxiv: 1
author:
- first_name: Sven Joscha
  full_name: Henheik, Sven Joscha
  id: 31d731d7-d235-11ea-ad11-b50331c8d7fb
  last_name: Henheik
  orcid: 0000-0003-1106-327X
- first_name: Asbjørn Bækgaard
  full_name: Lauritsen, Asbjørn Bækgaard
  id: e1a2682f-dc8d-11ea-abe3-81da9ac728f1
  last_name: Lauritsen
  orcid: 0000-0003-4476-2288
- first_name: Barbara
  full_name: Roos, Barbara
  id: 5DA90512-D80F-11E9-8994-2E2EE6697425
  last_name: Roos
  orcid: 0000-0002-9071-5880
citation:
  ama: Henheik SJ, Lauritsen AB, Roos B. Universality in low-dimensional BCS theory.
    <i>Reviews in Mathematical Physics</i>. 2023. doi:<a href="https://doi.org/10.1142/s0129055x2360005x">10.1142/s0129055x2360005x</a>
  apa: Henheik, S. J., Lauritsen, A. B., &#38; Roos, B. (2023). Universality in low-dimensional
    BCS theory. <i>Reviews in Mathematical Physics</i>. World Scientific Publishing.
    <a href="https://doi.org/10.1142/s0129055x2360005x">https://doi.org/10.1142/s0129055x2360005x</a>
  chicago: Henheik, Sven Joscha, Asbjørn Bækgaard Lauritsen, and Barbara Roos. “Universality
    in Low-Dimensional BCS Theory.” <i>Reviews in Mathematical Physics</i>. World
    Scientific Publishing, 2023. <a href="https://doi.org/10.1142/s0129055x2360005x">https://doi.org/10.1142/s0129055x2360005x</a>.
  ieee: S. J. Henheik, A. B. Lauritsen, and B. Roos, “Universality in low-dimensional
    BCS theory,” <i>Reviews in Mathematical Physics</i>. World Scientific Publishing,
    2023.
  ista: Henheik SJ, Lauritsen AB, Roos B. 2023. Universality in low-dimensional BCS
    theory. Reviews in Mathematical Physics., 2360005.
  mla: Henheik, Sven Joscha, et al. “Universality in Low-Dimensional BCS Theory.”
    <i>Reviews in Mathematical Physics</i>, 2360005, World Scientific Publishing,
    2023, doi:<a href="https://doi.org/10.1142/s0129055x2360005x">10.1142/s0129055x2360005x</a>.
  short: S.J. Henheik, A.B. Lauritsen, B. Roos, Reviews in Mathematical Physics (2023).
date_created: 2023-11-15T23:48:14Z
date_published: 2023-10-31T00:00:00Z
date_updated: 2023-11-20T10:04:38Z
day: '31'
department:
- _id: GradSch
- _id: LaEr
- _id: RoSe
doi: 10.1142/s0129055x2360005x
ec_funded: 1
external_id:
  arxiv:
  - '2301.05621'
has_accepted_license: '1'
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: https://doi.org/10.1142/S0129055X2360005X
month: '10'
oa: 1
oa_version: Published Version
project:
- _id: 62796744-2b32-11ec-9570-940b20777f1d
  call_identifier: H2020
  grant_number: '101020331'
  name: Random matrices beyond Wigner-Dyson-Mehta
- _id: bda63fe5-d553-11ed-ba76-a16e3d2f256b
  grant_number: I06427
  name: Mathematical Challenges in BCS Theory of Superconductivity
publication: Reviews in Mathematical Physics
publication_identifier:
  eissn:
  - 1793-6659
  issn:
  - 0129-055X
publication_status: epub_ahead
publisher: World Scientific Publishing
quality_controlled: '1'
scopus_import: '1'
status: public
title: Universality in low-dimensional BCS theory
tmp:
  image: /images/cc_by.png
  legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
  name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
  short: CC BY (4.0)
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
year: '2023'
...
---
_id: '12430'
abstract:
- lang: eng
  text: We study the time evolution of the Nelson model in a mean-field limit in which
    N nonrelativistic bosons weakly couple (with respect to the particle number) to
    a positive or zero mass quantized scalar field. Our main result is the derivation
    of the Bogoliubov dynamics and higher-order corrections. More precisely, we prove
    the convergence of the approximate wave function to the many-body wave function
    in norm, with a convergence rate proportional to the number of corrections taken
    into account in the approximation. We prove an analogous result for the unitary
    propagator. As an application, we derive a simple system of partial differential
    equations describing the time evolution of the first- and second-order approximations
    to the one-particle reduced density matrices of the particles and the quantum
    field, respectively.
article_number: '2350006'
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Marco
  full_name: Falconi, Marco
  last_name: Falconi
- first_name: Nikolai K
  full_name: Leopold, Nikolai K
  id: 4BC40BEC-F248-11E8-B48F-1D18A9856A87
  last_name: Leopold
  orcid: 0000-0002-0495-6822
- first_name: David Johannes
  full_name: Mitrouskas, David Johannes
  id: cbddacee-2b11-11eb-a02e-a2e14d04e52d
  last_name: Mitrouskas
- first_name: Sören P
  full_name: Petrat, Sören P
  id: 40AC02DC-F248-11E8-B48F-1D18A9856A87
  last_name: Petrat
  orcid: 0000-0002-9166-5889
citation:
  ama: Falconi M, Leopold NK, Mitrouskas DJ, Petrat SP. Bogoliubov dynamics and higher-order
    corrections for the regularized Nelson model. <i>Reviews in Mathematical Physics</i>.
    2023;35(4). doi:<a href="https://doi.org/10.1142/S0129055X2350006X">10.1142/S0129055X2350006X</a>
  apa: Falconi, M., Leopold, N. K., Mitrouskas, D. J., &#38; Petrat, S. P. (2023).
    Bogoliubov dynamics and higher-order corrections for the regularized Nelson model.
    <i>Reviews in Mathematical Physics</i>. World Scientific Publishing. <a href="https://doi.org/10.1142/S0129055X2350006X">https://doi.org/10.1142/S0129055X2350006X</a>
  chicago: Falconi, Marco, Nikolai K Leopold, David Johannes Mitrouskas, and Sören
    P Petrat. “Bogoliubov Dynamics and Higher-Order Corrections for the Regularized
    Nelson Model.” <i>Reviews in Mathematical Physics</i>. World Scientific Publishing,
    2023. <a href="https://doi.org/10.1142/S0129055X2350006X">https://doi.org/10.1142/S0129055X2350006X</a>.
  ieee: M. Falconi, N. K. Leopold, D. J. Mitrouskas, and S. P. Petrat, “Bogoliubov
    dynamics and higher-order corrections for the regularized Nelson model,” <i>Reviews
    in Mathematical Physics</i>, vol. 35, no. 4. World Scientific Publishing, 2023.
  ista: Falconi M, Leopold NK, Mitrouskas DJ, Petrat SP. 2023. Bogoliubov dynamics
    and higher-order corrections for the regularized Nelson model. Reviews in Mathematical
    Physics. 35(4), 2350006.
  mla: Falconi, Marco, et al. “Bogoliubov Dynamics and Higher-Order Corrections for
    the Regularized Nelson Model.” <i>Reviews in Mathematical Physics</i>, vol. 35,
    no. 4, 2350006, World Scientific Publishing, 2023, doi:<a href="https://doi.org/10.1142/S0129055X2350006X">10.1142/S0129055X2350006X</a>.
  short: M. Falconi, N.K. Leopold, D.J. Mitrouskas, S.P. Petrat, Reviews in Mathematical
    Physics 35 (2023).
date_created: 2023-01-29T23:00:59Z
date_published: 2023-01-09T00:00:00Z
date_updated: 2023-08-16T11:47:27Z
day: '09'
department:
- _id: RoSe
doi: 10.1142/S0129055X2350006X
external_id:
  arxiv:
  - '2110.00458'
  isi:
  - '000909760300001'
intvolume: '        35'
isi: 1
issue: '4'
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: ' https://doi.org/10.48550/arXiv.2110.00458'
month: '01'
oa: 1
oa_version: Preprint
publication: Reviews in Mathematical Physics
publication_identifier:
  issn:
  - 0129-055X
publication_status: published
publisher: World Scientific Publishing
quality_controlled: '1'
scopus_import: '1'
status: public
title: Bogoliubov dynamics and higher-order corrections for the regularized Nelson
  model
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 35
year: '2023'
...
---
_id: '10852'
abstract:
- lang: eng
  text: ' We review old and new results on the Fröhlich polaron model. The discussion
    includes the validity of the (classical) Pekar approximation in the strong coupling
    limit, quantum corrections to this limit, as well as the divergence of the effective
    polaron mass.'
acknowledgement: This work was supported by the European Research Council (ERC) under
  the Euro-pean Union’s Horizon 2020 research and innovation programme (grant agreementNo.
  694227).
article_number: '2060012'
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Robert
  full_name: Seiringer, Robert
  id: 4AFD0470-F248-11E8-B48F-1D18A9856A87
  last_name: Seiringer
  orcid: 0000-0002-6781-0521
citation:
  ama: Seiringer R. The polaron at strong coupling. <i>Reviews in Mathematical Physics</i>.
    2021;33(01). doi:<a href="https://doi.org/10.1142/s0129055x20600120">10.1142/s0129055x20600120</a>
  apa: Seiringer, R. (2021). The polaron at strong coupling. <i>Reviews in Mathematical
    Physics</i>. World Scientific Publishing. <a href="https://doi.org/10.1142/s0129055x20600120">https://doi.org/10.1142/s0129055x20600120</a>
  chicago: Seiringer, Robert. “The Polaron at Strong Coupling.” <i>Reviews in Mathematical
    Physics</i>. World Scientific Publishing, 2021. <a href="https://doi.org/10.1142/s0129055x20600120">https://doi.org/10.1142/s0129055x20600120</a>.
  ieee: R. Seiringer, “The polaron at strong coupling,” <i>Reviews in Mathematical
    Physics</i>, vol. 33, no. 01. World Scientific Publishing, 2021.
  ista: Seiringer R. 2021. The polaron at strong coupling. Reviews in Mathematical
    Physics. 33(01), 2060012.
  mla: Seiringer, Robert. “The Polaron at Strong Coupling.” <i>Reviews in Mathematical
    Physics</i>, vol. 33, no. 01, 2060012, World Scientific Publishing, 2021, doi:<a
    href="https://doi.org/10.1142/s0129055x20600120">10.1142/s0129055x20600120</a>.
  short: R. Seiringer, Reviews in Mathematical Physics 33 (2021).
date_created: 2022-03-18T08:11:34Z
date_published: 2021-02-01T00:00:00Z
date_updated: 2023-09-05T16:08:02Z
day: '01'
department:
- _id: RoSe
doi: 10.1142/s0129055x20600120
ec_funded: 1
external_id:
  arxiv:
  - '1912.12509'
  isi:
  - '000613313200013'
intvolume: '        33'
isi: 1
issue: '01'
keyword:
- Mathematical Physics
- Statistical and Nonlinear Physics
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: https://arxiv.org/abs/1912.12509
month: '02'
oa: 1
oa_version: Preprint
project:
- _id: 25C6DC12-B435-11E9-9278-68D0E5697425
  call_identifier: H2020
  grant_number: '694227'
  name: Analysis of quantum many-body systems
publication: Reviews in Mathematical Physics
publication_identifier:
  eissn:
  - 1793-6659
  issn:
  - 0129-055X
publication_status: published
publisher: World Scientific Publishing
quality_controlled: '1'
scopus_import: '1'
status: public
title: The polaron at strong coupling
type: journal_article
user_id: c635000d-4b10-11ee-a964-aac5a93f6ac1
volume: 33
year: '2021'
...
---
_id: '7900'
abstract:
- lang: eng
  text: Hartree–Fock theory has been justified as a mean-field approximation for fermionic
    systems. However, it suffers from some defects in predicting physical properties,
    making necessary a theory of quantum correlations. Recently, bosonization of many-body
    correlations has been rigorously justified as an upper bound on the correlation
    energy at high density with weak interactions. We review the bosonic approximation,
    deriving an effective Hamiltonian. We then show that for systems with Coulomb
    interaction this effective theory predicts collective excitations (plasmons) in
    accordance with the random phase approximation of Bohm and Pines, and with experimental
    observation.
article_number: '2060009'
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Niels P
  full_name: Benedikter, Niels P
  id: 3DE6C32A-F248-11E8-B48F-1D18A9856A87
  last_name: Benedikter
  orcid: 0000-0002-1071-6091
citation:
  ama: Benedikter NP. Bosonic collective excitations in Fermi gases. <i>Reviews in
    Mathematical Physics</i>. 2021;33(1). doi:<a href="https://doi.org/10.1142/s0129055x20600090">10.1142/s0129055x20600090</a>
  apa: Benedikter, N. P. (2021). Bosonic collective excitations in Fermi gases. <i>Reviews
    in Mathematical Physics</i>. World Scientific. <a href="https://doi.org/10.1142/s0129055x20600090">https://doi.org/10.1142/s0129055x20600090</a>
  chicago: Benedikter, Niels P. “Bosonic Collective Excitations in Fermi Gases.” <i>Reviews
    in Mathematical Physics</i>. World Scientific, 2021. <a href="https://doi.org/10.1142/s0129055x20600090">https://doi.org/10.1142/s0129055x20600090</a>.
  ieee: N. P. Benedikter, “Bosonic collective excitations in Fermi gases,” <i>Reviews
    in Mathematical Physics</i>, vol. 33, no. 1. World Scientific, 2021.
  ista: Benedikter NP. 2021. Bosonic collective excitations in Fermi gases. Reviews
    in Mathematical Physics. 33(1), 2060009.
  mla: Benedikter, Niels P. “Bosonic Collective Excitations in Fermi Gases.” <i>Reviews
    in Mathematical Physics</i>, vol. 33, no. 1, 2060009, World Scientific, 2021,
    doi:<a href="https://doi.org/10.1142/s0129055x20600090">10.1142/s0129055x20600090</a>.
  short: N.P. Benedikter, Reviews in Mathematical Physics 33 (2021).
date_created: 2020-05-28T16:47:55Z
date_published: 2021-01-01T00:00:00Z
date_updated: 2023-09-05T16:07:40Z
day: '01'
department:
- _id: RoSe
doi: 10.1142/s0129055x20600090
ec_funded: 1
external_id:
  arxiv:
  - '1910.08190'
  isi:
  - '000613313200010'
intvolume: '        33'
isi: 1
issue: '1'
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: https://arxiv.org/abs/1910.08190
month: '01'
oa: 1
oa_version: Preprint
project:
- _id: 25C6DC12-B435-11E9-9278-68D0E5697425
  call_identifier: H2020
  grant_number: '694227'
  name: Analysis of quantum many-body systems
publication: Reviews in Mathematical Physics
publication_identifier:
  eissn:
  - 1793-6659
  issn:
  - 0129-055X
publication_status: published
publisher: World Scientific
quality_controlled: '1'
scopus_import: '1'
status: public
title: Bosonic collective excitations in Fermi gases
type: journal_article
user_id: c635000d-4b10-11ee-a964-aac5a93f6ac1
volume: 33
year: '2021'
...
---
_id: '7685'
abstract:
- lang: eng
  text: We consider a gas of interacting bosons trapped in a box of side length one
    in the Gross–Pitaevskii limit. We review the proof of the validity of Bogoliubov’s
    prediction for the ground state energy and the low-energy excitation spectrum.
    This note is based on joint work with C. Brennecke, S. Cenatiempo and B. Schlein.
article_number: '2060006'
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Chiara
  full_name: Boccato, Chiara
  id: 342E7E22-F248-11E8-B48F-1D18A9856A87
  last_name: Boccato
citation:
  ama: Boccato C. The excitation spectrum of the Bose gas in the Gross-Pitaevskii
    regime. <i>Reviews in Mathematical Physics</i>. 2021;33(1). doi:<a href="https://doi.org/10.1142/S0129055X20600065">10.1142/S0129055X20600065</a>
  apa: Boccato, C. (2021). The excitation spectrum of the Bose gas in the Gross-Pitaevskii
    regime. <i>Reviews in Mathematical Physics</i>. World Scientific. <a href="https://doi.org/10.1142/S0129055X20600065">https://doi.org/10.1142/S0129055X20600065</a>
  chicago: Boccato, Chiara. “The Excitation Spectrum of the Bose Gas in the Gross-Pitaevskii
    Regime.” <i>Reviews in Mathematical Physics</i>. World Scientific, 2021. <a href="https://doi.org/10.1142/S0129055X20600065">https://doi.org/10.1142/S0129055X20600065</a>.
  ieee: C. Boccato, “The excitation spectrum of the Bose gas in the Gross-Pitaevskii
    regime,” <i>Reviews in Mathematical Physics</i>, vol. 33, no. 1. World Scientific,
    2021.
  ista: Boccato C. 2021. The excitation spectrum of the Bose gas in the Gross-Pitaevskii
    regime. Reviews in Mathematical Physics. 33(1), 2060006.
  mla: Boccato, Chiara. “The Excitation Spectrum of the Bose Gas in the Gross-Pitaevskii
    Regime.” <i>Reviews in Mathematical Physics</i>, vol. 33, no. 1, 2060006, World
    Scientific, 2021, doi:<a href="https://doi.org/10.1142/S0129055X20600065">10.1142/S0129055X20600065</a>.
  short: C. Boccato, Reviews in Mathematical Physics 33 (2021).
date_created: 2020-04-26T22:00:45Z
date_published: 2021-01-01T00:00:00Z
date_updated: 2023-08-04T10:50:13Z
day: '01'
department:
- _id: RoSe
doi: 10.1142/S0129055X20600065
ec_funded: 1
external_id:
  arxiv:
  - '2001.00497'
  isi:
  - '000613313200007'
intvolume: '        33'
isi: 1
issue: '1'
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: https://arxiv.org/abs/2001.00497
month: '01'
oa: 1
oa_version: Preprint
project:
- _id: 25C6DC12-B435-11E9-9278-68D0E5697425
  call_identifier: H2020
  grant_number: '694227'
  name: Analysis of quantum many-body systems
publication: Reviews in Mathematical Physics
publication_identifier:
  issn:
  - 0129-055X
publication_status: published
publisher: World Scientific
quality_controlled: '1'
scopus_import: '1'
status: public
title: The excitation spectrum of the Bose gas in the Gross-Pitaevskii regime
type: journal_article
user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
volume: 33
year: '2021'
...
---
_id: '9285'
abstract:
- lang: eng
  text: We first review the problem of a rigorous justification of Kubo’s formula
    for transport coefficients in gapped extended Hamiltonian quantum systems at zero
    temperature. In particular, the theoretical understanding of the quantum Hall
    effect rests on the validity of Kubo’s formula for such systems, a connection
    that we review briefly as well. We then highlight an approach to linear response
    theory based on non-equilibrium almost-stationary states (NEASS) and on a corresponding
    adiabatic theorem for such systems that was recently proposed and worked out by
    one of us in [51] for interacting fermionic systems on finite lattices. In the
    second part of our paper, we show how to lift the results of [51] to infinite
    systems by taking a thermodynamic limit.
article_number: '2060004'
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Sven Joscha
  full_name: Henheik, Sven Joscha
  id: 31d731d7-d235-11ea-ad11-b50331c8d7fb
  last_name: Henheik
  orcid: 0000-0003-1106-327X
- first_name: Stefan
  full_name: Teufel, Stefan
  last_name: Teufel
citation:
  ama: 'Henheik SJ, Teufel S. Justifying Kubo’s formula for gapped systems at zero
    temperature: A brief review and some new results. <i>Reviews in Mathematical Physics</i>.
    2021;33(01). doi:<a href="https://doi.org/10.1142/s0129055x20600041">10.1142/s0129055x20600041</a>'
  apa: 'Henheik, S. J., &#38; Teufel, S. (2021). Justifying Kubo’s formula for gapped
    systems at zero temperature: A brief review and some new results. <i>Reviews in
    Mathematical Physics</i>. World Scientific Publishing. <a href="https://doi.org/10.1142/s0129055x20600041">https://doi.org/10.1142/s0129055x20600041</a>'
  chicago: 'Henheik, Sven Joscha, and Stefan Teufel. “Justifying Kubo’s Formula for
    Gapped Systems at Zero Temperature: A Brief Review and Some New Results.” <i>Reviews
    in Mathematical Physics</i>. World Scientific Publishing, 2021. <a href="https://doi.org/10.1142/s0129055x20600041">https://doi.org/10.1142/s0129055x20600041</a>.'
  ieee: 'S. J. Henheik and S. Teufel, “Justifying Kubo’s formula for gapped systems
    at zero temperature: A brief review and some new results,” <i>Reviews in Mathematical
    Physics</i>, vol. 33, no. 01. World Scientific Publishing, 2021.'
  ista: 'Henheik SJ, Teufel S. 2021. Justifying Kubo’s formula for gapped systems
    at zero temperature: A brief review and some new results. Reviews in Mathematical
    Physics. 33(01), 2060004.'
  mla: 'Henheik, Sven Joscha, and Stefan Teufel. “Justifying Kubo’s Formula for Gapped
    Systems at Zero Temperature: A Brief Review and Some New Results.” <i>Reviews
    in Mathematical Physics</i>, vol. 33, no. 01, 2060004, World Scientific Publishing,
    2021, doi:<a href="https://doi.org/10.1142/s0129055x20600041">10.1142/s0129055x20600041</a>.'
  short: S.J. Henheik, S. Teufel, Reviews in Mathematical Physics 33 (2021).
date_created: 2021-03-26T11:29:46Z
date_published: 2021-02-01T00:00:00Z
date_updated: 2023-02-23T13:53:59Z
day: '01'
ddc:
- '500'
doi: 10.1142/s0129055x20600041
extern: '1'
external_id:
  arxiv:
  - '2002.08669'
has_accepted_license: '1'
intvolume: '        33'
issue: '01'
keyword:
- Mathematical Physics
- Statistical and Nonlinear Physics
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: https://arxiv.org/abs/2002.08669
month: '02'
oa: 1
oa_version: Preprint
publication: Reviews in Mathematical Physics
publication_identifier:
  issn:
  - 0129-055X
  - 1793-6659
publication_status: published
publisher: World Scientific Publishing
quality_controlled: '1'
scopus_import: '1'
status: public
title: 'Justifying Kubo’s formula for gapped systems at zero temperature: A brief
  review and some new results'
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 33
year: '2021'
...
---
_id: '2734'
abstract:
- lang: eng
  text: In this paper we describe an intrinsically geometric way of producing magnetic
    fields on S3 and R3 for which the corresponding Dirac operators have a non-trivial
    kernel. In many cases we are able to compute the dimension of the kernel. In particular
    we can give examples where the kernel has any given dimension. This generalizes
    the examples of Loss and Yau [1].
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: László
  full_name: Erdös, László
  id: 4DBD5372-F248-11E8-B48F-1D18A9856A87
  last_name: Erdös
  orcid: 0000-0001-5366-9603
- first_name: Jan
  full_name: Solovej, Jan
  last_name: Solovej
citation:
  ama: Erdös L, Solovej J. The kernel of Dirac operators on S3 and R3. <i>Reviews
    in Mathematical Physics</i>. 2001;13(10):1247-1280. doi:<a href="https://doi.org/10.1142/S0129055X01000983">10.1142/S0129055X01000983</a>
  apa: Erdös, L., &#38; Solovej, J. (2001). The kernel of Dirac operators on S3 and
    R3. <i>Reviews in Mathematical Physics</i>. World Scientific Publishing. <a href="https://doi.org/10.1142/S0129055X01000983">https://doi.org/10.1142/S0129055X01000983</a>
  chicago: Erdös, László, and Jan Solovej. “The Kernel of Dirac Operators on S3 and
    R3.” <i>Reviews in Mathematical Physics</i>. World Scientific Publishing, 2001.
    <a href="https://doi.org/10.1142/S0129055X01000983">https://doi.org/10.1142/S0129055X01000983</a>.
  ieee: L. Erdös and J. Solovej, “The kernel of Dirac operators on S3 and R3,” <i>Reviews
    in Mathematical Physics</i>, vol. 13, no. 10. World Scientific Publishing, pp.
    1247–1280, 2001.
  ista: Erdös L, Solovej J. 2001. The kernel of Dirac operators on S3 and R3. Reviews
    in Mathematical Physics. 13(10), 1247–1280.
  mla: Erdös, László, and Jan Solovej. “The Kernel of Dirac Operators on S3 and R3.”
    <i>Reviews in Mathematical Physics</i>, vol. 13, no. 10, World Scientific Publishing,
    2001, pp. 1247–80, doi:<a href="https://doi.org/10.1142/S0129055X01000983">10.1142/S0129055X01000983</a>.
  short: L. Erdös, J. Solovej, Reviews in Mathematical Physics 13 (2001) 1247–1280.
date_created: 2018-12-11T11:59:19Z
date_published: 2001-10-01T00:00:00Z
date_updated: 2023-05-16T12:24:25Z
day: '01'
doi: 10.1142/S0129055X01000983
extern: '1'
external_id:
  arxiv:
  - math-ph/0001036
intvolume: '        13'
issue: '10'
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: https://arxiv.org/abs/math-ph/0001036
month: '10'
oa: 1
oa_version: Published Version
page: 1247 - 1280
publication: Reviews in Mathematical Physics
publication_identifier:
  issn:
  - 0129-055X
publication_status: published
publisher: World Scientific Publishing
publist_id: '4158'
quality_controlled: '1'
scopus_import: '1'
status: public
title: The kernel of Dirac operators on S3 and R3
type: journal_article
user_id: ea97e931-d5af-11eb-85d4-e6957dddbf17
volume: 13
year: '2001'
...