---
_id: '8816'
abstract:
- lang: eng
  text: Area-dependent quantum field theory is a modification of two-dimensional topological
    quantum field theory, where one equips each connected component of a bordism with
    a positive real number—interpreted as area—which behaves additively under glueing.
    As opposed to topological theories, in area-dependent theories the state spaces
    can be infinite-dimensional. We introduce the notion of regularised Frobenius
    algebras in Hilbert spaces and show that area-dependent theories are in one-to-one
    correspondence to commutative regularised Frobenius algebras. We also provide
    a state sum construction for area-dependent theories. Our main example is two-dimensional
    Yang–Mills theory with compact gauge group, which we treat in detail.
acknowledgement: The authors thank Yuki Arano, Nils Carqueville, Alexei Davydov, Reiner
  Lauterbach, Pau Enrique Moliner, Chris Heunen, André Henriques, Ehud Meir, Catherine
  Meusburger, Gregor Schaumann, Richard Szabo and Stefan Wagner for helpful discussions
  and comments. We also thank the referees for their detailed comments which significantly
  improved the exposition of this paper. LS is supported by the DFG Research Training
  Group 1670 “Mathematics Inspired by String Theory and Quantum Field Theory”. Open
  access funding provided by Institute of Science and Technology (IST Austria).
article_processing_charge: Yes (via OA deal)
article_type: original
author:
- first_name: Ingo
  full_name: Runkel, Ingo
  last_name: Runkel
- first_name: Lorant
  full_name: Szegedy, Lorant
  id: 7943226E-220E-11EA-94C7-D59F3DDC885E
  last_name: Szegedy
  orcid: 0000-0003-2834-5054
citation:
  ama: Runkel I, Szegedy L. Area-dependent quantum field theory. <i>Communications
    in Mathematical Physics</i>. 2021;381(1):83–117. doi:<a href="https://doi.org/10.1007/s00220-020-03902-1">10.1007/s00220-020-03902-1</a>
  apa: Runkel, I., &#38; Szegedy, L. (2021). Area-dependent quantum field theory.
    <i>Communications in Mathematical Physics</i>. Springer Nature. <a href="https://doi.org/10.1007/s00220-020-03902-1">https://doi.org/10.1007/s00220-020-03902-1</a>
  chicago: Runkel, Ingo, and Lorant Szegedy. “Area-Dependent Quantum Field Theory.”
    <i>Communications in Mathematical Physics</i>. Springer Nature, 2021. <a href="https://doi.org/10.1007/s00220-020-03902-1">https://doi.org/10.1007/s00220-020-03902-1</a>.
  ieee: I. Runkel and L. Szegedy, “Area-dependent quantum field theory,” <i>Communications
    in Mathematical Physics</i>, vol. 381, no. 1. Springer Nature, pp. 83–117, 2021.
  ista: Runkel I, Szegedy L. 2021. Area-dependent quantum field theory. Communications
    in Mathematical Physics. 381(1), 83–117.
  mla: Runkel, Ingo, and Lorant Szegedy. “Area-Dependent Quantum Field Theory.” <i>Communications
    in Mathematical Physics</i>, vol. 381, no. 1, Springer Nature, 2021, pp. 83–117,
    doi:<a href="https://doi.org/10.1007/s00220-020-03902-1">10.1007/s00220-020-03902-1</a>.
  short: I. Runkel, L. Szegedy, Communications in Mathematical Physics 381 (2021)
    83–117.
date_created: 2020-11-29T23:01:17Z
date_published: 2021-01-01T00:00:00Z
date_updated: 2023-08-04T11:13:35Z
day: '01'
ddc:
- '510'
department:
- _id: MiLe
doi: 10.1007/s00220-020-03902-1
external_id:
  isi:
  - '000591139000001'
file:
- access_level: open_access
  checksum: 6f451f9c2b74bedbc30cf884a3e02670
  content_type: application/pdf
  creator: dernst
  date_created: 2021-02-03T15:00:30Z
  date_updated: 2021-02-03T15:00:30Z
  file_id: '9081'
  file_name: 2021_CommMathPhys_Runkel.pdf
  file_size: 790526
  relation: main_file
  success: 1
file_date_updated: 2021-02-03T15:00:30Z
has_accepted_license: '1'
intvolume: '       381'
isi: 1
issue: '1'
language:
- iso: eng
license: https://creativecommons.org/licenses/by/4.0/
month: '01'
oa: 1
oa_version: Published Version
page: 83–117
project:
- _id: B67AFEDC-15C9-11EA-A837-991A96BB2854
  name: IST Austria Open Access Fund
publication: Communications in Mathematical Physics
publication_identifier:
  eissn:
  - '14320916'
  issn:
  - '00103616'
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
status: public
title: Area-dependent quantum field 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: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
volume: 381
year: '2021'
...
---
_id: '8325'
abstract:
- lang: eng
  text: "Let \U0001D439:ℤ2→ℤ be the pointwise minimum of several linear functions.
    The theory of smoothing allows us to prove that under certain conditions there
    exists the pointwise minimal function among all integer-valued superharmonic functions
    coinciding with F “at infinity”. We develop such a theory to prove existence of
    so-called solitons (or strings) in a sandpile model, studied by S. Caracciolo,
    G. Paoletti, and A. Sportiello. Thus we made a step towards understanding the
    phenomena of the identity in the sandpile group for planar domains where solitons
    appear according to experiments. We prove that sandpile states, defined using
    our smoothing procedure, move changeless when we apply the wave operator (that
    is why we call them solitons), and can interact, forming triads and nodes. "
acknowledgement: We thank Andrea Sportiello for sharing his insights on perturbative
  regimes of the Abelian sandpile model which was the starting point of our work.
  We also thank Grigory Mikhalkin, who encouraged us to approach this problem. We
  thank an anonymous referee. Also we thank Misha Khristoforov and Sergey Lanzat who
  participated on the initial state of this project, when we had nothing except the
  computer simulation and pictures. We thank Mikhail Raskin for providing us the code
  on Golly for faster simulations. Ilia Zharkov, Ilia Itenberg, Kristin Shaw, Max
  Karev, Lionel Levine, Ernesto Lupercio, Pavol Ševera, Yulieth Prieto, Michael Polyak,
  Danila Cherkashin asked us a lot of questions and listened to us; not all of their
  questions found answers here, but we are going to treat them in subsequent papers.
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Nikita
  full_name: Kalinin, Nikita
  last_name: Kalinin
- first_name: Mikhail
  full_name: Shkolnikov, Mikhail
  id: 35084A62-F248-11E8-B48F-1D18A9856A87
  last_name: Shkolnikov
  orcid: 0000-0002-4310-178X
citation:
  ama: Kalinin N, Shkolnikov M. Sandpile solitons via smoothing of superharmonic functions.
    <i>Communications in Mathematical Physics</i>. 2020;378(9):1649-1675. doi:<a href="https://doi.org/10.1007/s00220-020-03828-8">10.1007/s00220-020-03828-8</a>
  apa: Kalinin, N., &#38; Shkolnikov, M. (2020). Sandpile solitons via smoothing of
    superharmonic functions. <i>Communications in Mathematical Physics</i>. Springer
    Nature. <a href="https://doi.org/10.1007/s00220-020-03828-8">https://doi.org/10.1007/s00220-020-03828-8</a>
  chicago: Kalinin, Nikita, and Mikhail Shkolnikov. “Sandpile Solitons via Smoothing
    of Superharmonic Functions.” <i>Communications in Mathematical Physics</i>. Springer
    Nature, 2020. <a href="https://doi.org/10.1007/s00220-020-03828-8">https://doi.org/10.1007/s00220-020-03828-8</a>.
  ieee: N. Kalinin and M. Shkolnikov, “Sandpile solitons via smoothing of superharmonic
    functions,” <i>Communications in Mathematical Physics</i>, vol. 378, no. 9. Springer
    Nature, pp. 1649–1675, 2020.
  ista: Kalinin N, Shkolnikov M. 2020. Sandpile solitons via smoothing of superharmonic
    functions. Communications in Mathematical Physics. 378(9), 1649–1675.
  mla: Kalinin, Nikita, and Mikhail Shkolnikov. “Sandpile Solitons via Smoothing of
    Superharmonic Functions.” <i>Communications in Mathematical Physics</i>, vol.
    378, no. 9, Springer Nature, 2020, pp. 1649–75, doi:<a href="https://doi.org/10.1007/s00220-020-03828-8">10.1007/s00220-020-03828-8</a>.
  short: N. Kalinin, M. Shkolnikov, Communications in Mathematical Physics 378 (2020)
    1649–1675.
date_created: 2020-08-30T22:01:13Z
date_published: 2020-09-01T00:00:00Z
date_updated: 2023-08-22T09:00:03Z
day: '01'
department:
- _id: TaHa
doi: 10.1007/s00220-020-03828-8
ec_funded: 1
external_id:
  arxiv:
  - '1711.04285'
  isi:
  - '000560620600001'
intvolume: '       378'
isi: 1
issue: '9'
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: https://arxiv.org/abs/1711.04285
month: '09'
oa: 1
oa_version: Preprint
page: 1649-1675
project:
- _id: 25681D80-B435-11E9-9278-68D0E5697425
  call_identifier: FP7
  grant_number: '291734'
  name: International IST Postdoc Fellowship Programme
publication: Communications in Mathematical Physics
publication_identifier:
  eissn:
  - '14320916'
  issn:
  - '00103616'
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
status: public
title: Sandpile solitons via smoothing of superharmonic functions
type: journal_article
user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
volume: 378
year: '2020'
...
---
_id: '554'
abstract:
- lang: eng
  text: We analyse the canonical Bogoliubov free energy functional in three dimensions
    at low temperatures in the dilute limit. We prove existence of a first-order phase
    transition and, in the limit (Formula presented.), we determine the critical temperature
    to be (Formula presented.) to leading order. Here, (Formula presented.) is the
    critical temperature of the free Bose gas, ρ is the density of the gas and a is
    the scattering length of the pair-interaction potential V. We also prove asymptotic
    expansions for the free energy. In particular, we recover the Lee–Huang–Yang formula
    in the limit (Formula presented.).
arxiv: 1
author:
- first_name: Marcin M
  full_name: Napiórkowski, Marcin M
  id: 4197AD04-F248-11E8-B48F-1D18A9856A87
  last_name: Napiórkowski
- first_name: Robin
  full_name: Reuvers, Robin
  last_name: Reuvers
- first_name: Jan
  full_name: Solovej, Jan
  last_name: Solovej
citation:
  ama: 'Napiórkowski MM, Reuvers R, Solovej J. The Bogoliubov free energy functional
    II: The dilute Limit. <i>Communications in Mathematical Physics</i>. 2018;360(1):347-403.
    doi:<a href="https://doi.org/10.1007/s00220-017-3064-x">10.1007/s00220-017-3064-x</a>'
  apa: 'Napiórkowski, M. M., Reuvers, R., &#38; Solovej, J. (2018). The Bogoliubov
    free energy functional II: The dilute Limit. <i>Communications in Mathematical
    Physics</i>. Springer. <a href="https://doi.org/10.1007/s00220-017-3064-x">https://doi.org/10.1007/s00220-017-3064-x</a>'
  chicago: 'Napiórkowski, Marcin M, Robin Reuvers, and Jan Solovej. “The Bogoliubov
    Free Energy Functional II: The Dilute Limit.” <i>Communications in Mathematical
    Physics</i>. Springer, 2018. <a href="https://doi.org/10.1007/s00220-017-3064-x">https://doi.org/10.1007/s00220-017-3064-x</a>.'
  ieee: 'M. M. Napiórkowski, R. Reuvers, and J. Solovej, “The Bogoliubov free energy
    functional II: The dilute Limit,” <i>Communications in Mathematical Physics</i>,
    vol. 360, no. 1. Springer, pp. 347–403, 2018.'
  ista: 'Napiórkowski MM, Reuvers R, Solovej J. 2018. The Bogoliubov free energy functional
    II: The dilute Limit. Communications in Mathematical Physics. 360(1), 347–403.'
  mla: 'Napiórkowski, Marcin M., et al. “The Bogoliubov Free Energy Functional II:
    The Dilute Limit.” <i>Communications in Mathematical Physics</i>, vol. 360, no.
    1, Springer, 2018, pp. 347–403, doi:<a href="https://doi.org/10.1007/s00220-017-3064-x">10.1007/s00220-017-3064-x</a>.'
  short: M.M. Napiórkowski, R. Reuvers, J. Solovej, Communications in Mathematical
    Physics 360 (2018) 347–403.
date_created: 2018-12-11T11:47:09Z
date_published: 2018-05-01T00:00:00Z
date_updated: 2021-01-12T08:02:35Z
day: '01'
department:
- _id: RoSe
doi: 10.1007/s00220-017-3064-x
external_id:
  arxiv:
  - '1511.05953'
intvolume: '       360'
issue: '1'
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: https://arxiv.org/abs/1511.05953
month: '05'
oa: 1
oa_version: Submitted Version
page: 347-403
project:
- _id: 25C878CE-B435-11E9-9278-68D0E5697425
  call_identifier: FWF
  grant_number: P27533_N27
  name: Structure of the Excitation Spectrum for Many-Body Quantum Systems
publication: Communications in Mathematical Physics
publication_identifier:
  issn:
  - '00103616'
publication_status: published
publisher: Springer
publist_id: '7260'
quality_controlled: '1'
scopus_import: 1
status: public
title: 'The Bogoliubov free energy functional II: The dilute Limit'
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 360
year: '2018'
...
---
_id: '741'
abstract:
- lang: eng
  text: We prove that a system of N fermions interacting with an additional particle
    via point interactions is stable if the ratio of the mass of the additional particle
    to the one of the fermions is larger than some critical m*. The value of m* is
    independent of N and turns out to be less than 1. This fact has important implications
    for the stability of the unitary Fermi gas. We also characterize the domain of
    the Hamiltonian of this model, and establish the validity of the Tan relations
    for all wave functions in the domain.
article_processing_charge: No
author:
- first_name: Thomas
  full_name: Moser, Thomas
  id: 2B5FC9A4-F248-11E8-B48F-1D18A9856A87
  last_name: Moser
- first_name: Robert
  full_name: Seiringer, Robert
  id: 4AFD0470-F248-11E8-B48F-1D18A9856A87
  last_name: Seiringer
  orcid: 0000-0002-6781-0521
citation:
  ama: Moser T, Seiringer R. Stability of a fermionic N+1 particle system with point
    interactions. <i>Communications in Mathematical Physics</i>. 2017;356(1):329-355.
    doi:<a href="https://doi.org/10.1007/s00220-017-2980-0">10.1007/s00220-017-2980-0</a>
  apa: Moser, T., &#38; Seiringer, R. (2017). Stability of a fermionic N+1 particle
    system with point interactions. <i>Communications in Mathematical Physics</i>.
    Springer. <a href="https://doi.org/10.1007/s00220-017-2980-0">https://doi.org/10.1007/s00220-017-2980-0</a>
  chicago: Moser, Thomas, and Robert Seiringer. “Stability of a Fermionic N+1 Particle
    System with Point Interactions.” <i>Communications in Mathematical Physics</i>.
    Springer, 2017. <a href="https://doi.org/10.1007/s00220-017-2980-0">https://doi.org/10.1007/s00220-017-2980-0</a>.
  ieee: T. Moser and R. Seiringer, “Stability of a fermionic N+1 particle system with
    point interactions,” <i>Communications in Mathematical Physics</i>, vol. 356,
    no. 1. Springer, pp. 329–355, 2017.
  ista: Moser T, Seiringer R. 2017. Stability of a fermionic N+1 particle system with
    point interactions. Communications in Mathematical Physics. 356(1), 329–355.
  mla: Moser, Thomas, and Robert Seiringer. “Stability of a Fermionic N+1 Particle
    System with Point Interactions.” <i>Communications in Mathematical Physics</i>,
    vol. 356, no. 1, Springer, 2017, pp. 329–55, doi:<a href="https://doi.org/10.1007/s00220-017-2980-0">10.1007/s00220-017-2980-0</a>.
  short: T. Moser, R. Seiringer, Communications in Mathematical Physics 356 (2017)
    329–355.
date_created: 2018-12-11T11:48:15Z
date_published: 2017-11-01T00:00:00Z
date_updated: 2023-09-27T12:34:15Z
day: '01'
ddc:
- '539'
department:
- _id: RoSe
doi: 10.1007/s00220-017-2980-0
ec_funded: 1
external_id:
  isi:
  - '000409821300010'
file:
- access_level: open_access
  checksum: 0fd9435400f91e9b3c5346319a2d24e3
  content_type: application/pdf
  creator: system
  date_created: 2018-12-12T10:10:50Z
  date_updated: 2020-07-14T12:47:57Z
  file_id: '4841'
  file_name: IST-2017-880-v1+1_s00220-017-2980-0.pdf
  file_size: 952639
  relation: main_file
file_date_updated: 2020-07-14T12:47:57Z
has_accepted_license: '1'
intvolume: '       356'
isi: 1
issue: '1'
language:
- iso: eng
month: '11'
oa: 1
oa_version: Published Version
page: 329 - 355
project:
- _id: 25C6DC12-B435-11E9-9278-68D0E5697425
  call_identifier: H2020
  grant_number: '694227'
  name: Analysis of quantum many-body systems
- _id: 25C878CE-B435-11E9-9278-68D0E5697425
  call_identifier: FWF
  grant_number: P27533_N27
  name: Structure of the Excitation Spectrum for Many-Body Quantum Systems
publication: Communications in Mathematical Physics
publication_identifier:
  issn:
  - '00103616'
publication_status: published
publisher: Springer
publist_id: '6926'
pubrep_id: '880'
quality_controlled: '1'
related_material:
  record:
  - id: '52'
    relation: dissertation_contains
    status: public
scopus_import: '1'
status: public
title: Stability of a fermionic N+1 particle system with point interactions
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: c635000d-4b10-11ee-a964-aac5a93f6ac1
volume: 356
year: '2017'
...
---
_id: '1207'
abstract:
- lang: eng
  text: The eigenvalue distribution of the sum of two large Hermitian matrices, when
    one of them is conjugated by a Haar distributed unitary matrix, is asymptotically
    given by the free convolution of their spectral distributions. We prove that this
    convergence also holds locally in the bulk of the spectrum, down to the optimal
    scales larger than the eigenvalue spacing. The corresponding eigenvectors are
    fully delocalized. Similar results hold for the sum of two real symmetric matrices,
    when one is conjugated by Haar orthogonal matrix.
article_processing_charge: Yes (via OA deal)
author:
- first_name: Zhigang
  full_name: Bao, Zhigang
  id: 442E6A6C-F248-11E8-B48F-1D18A9856A87
  last_name: Bao
  orcid: 0000-0003-3036-1475
- first_name: László
  full_name: Erdös, László
  id: 4DBD5372-F248-11E8-B48F-1D18A9856A87
  last_name: Erdös
  orcid: 0000-0001-5366-9603
- first_name: Kevin
  full_name: Schnelli, Kevin
  id: 434AD0AE-F248-11E8-B48F-1D18A9856A87
  last_name: Schnelli
  orcid: 0000-0003-0954-3231
citation:
  ama: Bao Z, Erdös L, Schnelli K. Local law of addition of random matrices on optimal
    scale. <i>Communications in Mathematical Physics</i>. 2017;349(3):947-990. doi:<a
    href="https://doi.org/10.1007/s00220-016-2805-6">10.1007/s00220-016-2805-6</a>
  apa: Bao, Z., Erdös, L., &#38; Schnelli, K. (2017). Local law of addition of random
    matrices on optimal scale. <i>Communications in Mathematical Physics</i>. Springer.
    <a href="https://doi.org/10.1007/s00220-016-2805-6">https://doi.org/10.1007/s00220-016-2805-6</a>
  chicago: Bao, Zhigang, László Erdös, and Kevin Schnelli. “Local Law of Addition
    of Random Matrices on Optimal Scale.” <i>Communications in Mathematical Physics</i>.
    Springer, 2017. <a href="https://doi.org/10.1007/s00220-016-2805-6">https://doi.org/10.1007/s00220-016-2805-6</a>.
  ieee: Z. Bao, L. Erdös, and K. Schnelli, “Local law of addition of random matrices
    on optimal scale,” <i>Communications in Mathematical Physics</i>, vol. 349, no.
    3. Springer, pp. 947–990, 2017.
  ista: Bao Z, Erdös L, Schnelli K. 2017. Local law of addition of random matrices
    on optimal scale. Communications in Mathematical Physics. 349(3), 947–990.
  mla: Bao, Zhigang, et al. “Local Law of Addition of Random Matrices on Optimal Scale.”
    <i>Communications in Mathematical Physics</i>, vol. 349, no. 3, Springer, 2017,
    pp. 947–90, doi:<a href="https://doi.org/10.1007/s00220-016-2805-6">10.1007/s00220-016-2805-6</a>.
  short: Z. Bao, L. Erdös, K. Schnelli, Communications in Mathematical Physics 349
    (2017) 947–990.
date_created: 2018-12-11T11:50:43Z
date_published: 2017-02-01T00:00:00Z
date_updated: 2023-09-20T11:16:57Z
day: '01'
ddc:
- '530'
department:
- _id: LaEr
doi: 10.1007/s00220-016-2805-6
ec_funded: 1
external_id:
  isi:
  - '000393696700005'
file:
- access_level: open_access
  checksum: ddff79154c3daf27237de5383b1264a9
  content_type: application/pdf
  creator: system
  date_created: 2018-12-12T10:14:47Z
  date_updated: 2020-07-14T12:44:39Z
  file_id: '5102'
  file_name: IST-2016-722-v1+1_s00220-016-2805-6.pdf
  file_size: 1033743
  relation: main_file
file_date_updated: 2020-07-14T12:44:39Z
has_accepted_license: '1'
intvolume: '       349'
isi: 1
issue: '3'
language:
- iso: eng
month: '02'
oa: 1
oa_version: Published Version
page: 947 - 990
project:
- _id: 258DCDE6-B435-11E9-9278-68D0E5697425
  call_identifier: FP7
  grant_number: '338804'
  name: Random matrices, universality and disordered quantum systems
publication: Communications in Mathematical Physics
publication_identifier:
  issn:
  - '00103616'
publication_status: published
publisher: Springer
publist_id: '6141'
pubrep_id: '722'
quality_controlled: '1'
scopus_import: '1'
status: public
title: Local law of addition of random matrices on optimal scale
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: c635000d-4b10-11ee-a964-aac5a93f6ac1
volume: 349
year: '2017'
...