---
_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. Communications
in Mathematical Physics. 2021;381(1):83–117. doi:10.1007/s00220-020-03902-1
apa: Runkel, I., & Szegedy, L. (2021). Area-dependent quantum field theory.
Communications in Mathematical Physics. Springer Nature. https://doi.org/10.1007/s00220-020-03902-1
chicago: Runkel, Ingo, and Lorant Szegedy. “Area-Dependent Quantum Field Theory.”
Communications in Mathematical Physics. Springer Nature, 2021. https://doi.org/10.1007/s00220-020-03902-1.
ieee: I. Runkel and L. Szegedy, “Area-dependent quantum field theory,” Communications
in Mathematical Physics, 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.” Communications
in Mathematical Physics, vol. 381, no. 1, Springer Nature, 2021, pp. 83–117,
doi:10.1007/s00220-020-03902-1.
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
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
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.
Communications in Mathematical Physics. 2020;378(9):1649-1675. doi:10.1007/s00220-020-03828-8
apa: Kalinin, N., & Shkolnikov, M. (2020). Sandpile solitons via smoothing of
superharmonic functions. Communications in Mathematical Physics. Springer
Nature. https://doi.org/10.1007/s00220-020-03828-8
chicago: Kalinin, Nikita, and Mikhail Shkolnikov. “Sandpile Solitons via Smoothing
of Superharmonic Functions.” Communications in Mathematical Physics. Springer
Nature, 2020. https://doi.org/10.1007/s00220-020-03828-8.
ieee: N. Kalinin and M. Shkolnikov, “Sandpile solitons via smoothing of superharmonic
functions,” Communications in Mathematical Physics, 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.” Communications in Mathematical Physics, vol.
378, no. 9, Springer Nature, 2020, pp. 1649–75, doi:10.1007/s00220-020-03828-8.
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.).
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. Communications in Mathematical Physics. 2018;360(1):347-403.
doi:10.1007/s00220-017-3064-x'
apa: 'Napiórkowski, M. M., Reuvers, R., & Solovej, J. (2018). The Bogoliubov
free energy functional II: The dilute Limit. Communications in Mathematical
Physics. Springer. https://doi.org/10.1007/s00220-017-3064-x'
chicago: 'Napiórkowski, Marcin M, Robin Reuvers, and Jan Solovej. “The Bogoliubov
Free Energy Functional II: The Dilute Limit.” Communications in Mathematical
Physics. Springer, 2018. https://doi.org/10.1007/s00220-017-3064-x.'
ieee: 'M. M. Napiórkowski, R. Reuvers, and J. Solovej, “The Bogoliubov free energy
functional II: The dilute Limit,” Communications in Mathematical Physics,
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.” Communications in Mathematical Physics, vol. 360, no.
1, Springer, 2018, pp. 347–403, doi:10.1007/s00220-017-3064-x.'
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: '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. Communications in Mathematical Physics. 2017;349(3):947-990. doi:10.1007/s00220-016-2805-6
apa: Bao, Z., Erdös, L., & Schnelli, K. (2017). Local law of addition of random
matrices on optimal scale. Communications in Mathematical Physics. Springer.
https://doi.org/10.1007/s00220-016-2805-6
chicago: Bao, Zhigang, László Erdös, and Kevin Schnelli. “Local Law of Addition
of Random Matrices on Optimal Scale.” Communications in Mathematical Physics.
Springer, 2017. https://doi.org/10.1007/s00220-016-2805-6.
ieee: Z. Bao, L. Erdös, and K. Schnelli, “Local law of addition of random matrices
on optimal scale,” Communications in Mathematical Physics, 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.”
Communications in Mathematical Physics, vol. 349, no. 3, Springer, 2017,
pp. 947–90, doi:10.1007/s00220-016-2805-6.
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'
...
---
_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. Communications in Mathematical Physics. 2017;356(1):329-355.
doi:10.1007/s00220-017-2980-0
apa: Moser, T., & Seiringer, R. (2017). Stability of a fermionic N+1 particle
system with point interactions. Communications in Mathematical Physics.
Springer. https://doi.org/10.1007/s00220-017-2980-0
chicago: Moser, Thomas, and Robert Seiringer. “Stability of a Fermionic N+1 Particle
System with Point Interactions.” Communications in Mathematical Physics.
Springer, 2017. https://doi.org/10.1007/s00220-017-2980-0.
ieee: T. Moser and R. Seiringer, “Stability of a fermionic N+1 particle system with
point interactions,” Communications in Mathematical Physics, 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.” Communications in Mathematical Physics,
vol. 356, no. 1, Springer, 2017, pp. 329–55, doi:10.1007/s00220-017-2980-0.
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'
...