---
_id: '1452'
abstract:
- lang: eng
text: 'In this Note we present pairs of hyperkähler orbifolds which satisfy two
different versions of mirror symmetry. On the one hand, we show that their Hodge
numbers (or more precisely, stringy E-polynomials) are equal. On the other hand,
we show that they satisfy the prescription of Strominger, Yau, and Zaslow (which
in the present case goes back to Bershadsky, Johansen, Sadov and Vafa): that a
Calabi-Yau and its mirror should fiber over the same real manifold, with special
Lagrangian fibers which are tori dual to each other. Our examples arise as moduli
spaces of local systems on a curve with structure group SL(n); the mirror is the
corresponding space with structure group PGL(n). The special Lagrangian tori come
from an algebraically completely integrable Hamiltonian system: the Hitchin system.'
author:
- first_name: Tamas
full_name: Tamas Hausel
id: 4A0666D8-F248-11E8-B48F-1D18A9856A87
last_name: Hausel
- first_name: Michael
full_name: Thaddeus, Michael
last_name: Thaddeus
citation:
ama: 'Hausel T, Thaddeus M. Examples of mirror partners arising from integrable
systems. *Comptes Rendus de l’Academie des Sciences - Series I: Mathematics*.
2001;333(4):313-318. doi:10.1016/S0764-4442(01)02057-2'
apa: 'Hausel, T., & Thaddeus, M. (2001). Examples of mirror partners arising
from integrable systems. *Comptes Rendus de l’Academie Des Sciences - Series
I: Mathematics*. Elsevier. https://doi.org/10.1016/S0764-4442(01)02057-2'
chicago: 'Hausel, Tamás, and Michael Thaddeus. “Examples of Mirror Partners Arising
from Integrable Systems.” *Comptes Rendus de l’Academie Des Sciences - Series
I: Mathematics*. Elsevier, 2001. https://doi.org/10.1016/S0764-4442(01)02057-2.'
ieee: 'T. Hausel and M. Thaddeus, “Examples of mirror partners arising from integrable
systems,” *Comptes Rendus de l’Academie des Sciences - Series I: Mathematics*,
vol. 333, no. 4. Elsevier, pp. 313–318, 2001.'
ista: 'Hausel T, Thaddeus M. 2001. Examples of mirror partners arising from integrable
systems. Comptes Rendus de l’Academie des Sciences - Series I: Mathematics. 333(4),
313–318.'
mla: 'Hausel, Tamás, and Michael Thaddeus. “Examples of Mirror Partners Arising
from Integrable Systems.” *Comptes Rendus de l’Academie Des Sciences - Series
I: Mathematics*, vol. 333, no. 4, Elsevier, 2001, pp. 313–18, doi:10.1016/S0764-4442(01)02057-2.'
short: 'T. Hausel, M. Thaddeus, Comptes Rendus de l’Academie Des Sciences - Series
I: Mathematics 333 (2001) 313–318.'
date_created: 2018-12-11T11:52:06Z
date_published: 2001-08-15T00:00:00Z
date_updated: 2021-01-12T06:50:51Z
day: '15'
doi: 10.1016/S0764-4442(01)02057-2
extern: 1
intvolume: ' 333'
issue: '4'
main_file_link:
- open_access: '1'
url: http://arxiv.org/abs/math/0106140
month: '08'
oa: 1
page: 313 - 318
publication: 'Comptes Rendus de l''Academie des Sciences - Series I: Mathematics'
publication_status: published
publisher: Elsevier
publist_id: '5742'
quality_controlled: 0
status: public
title: Examples of mirror partners arising from integrable systems
type: journal_article
volume: 333
year: '2001'
...
---
_id: '1453'
abstract:
- lang: eng
text: In this Letter we exhibit a one-parameter family of new Taub-NUT instantons
parameterized by a half-line. The endpoint of the half-line will be the reducible
Yang-Mills instanton corresponding to the Eguchi-Hanson-Gibbons L2 harmonic 2-form,
while at an inner point we recover the Pope-Yuille instanton constructed as a
projection of the Levi-Civitá connection onto the positive su(2)+ ⊂ so(4) subalgebra.
Our method imitates the Jackiw-Nohl-Rebbi construction originally designed for
flat R4. That is we find a one-parameter family of harmonic functions on the Taub-NUT
space with a point singularity, rescale the metric and project the obtained Levi-Civitá
connection onto the other negative su(2)- ⊂ so(4) part. Our solutions will possess
the full U(2) symmetry, and thus provide more solutions to the recently proposed
U(2) symmetric ansatz of Kim and Yoon.
acknowledgement: We would like to acknowledge the financial support provided by the
Miller Institute of Basic Research in Science, the Japan Society for the Promotion
of Science, grant No. P99736 and the partial support by OTKA grant No. T032478.
author:
- first_name: Gábor
full_name: Etesi, Gábor
last_name: Etesi
- first_name: Tamas
full_name: Tamas Hausel
id: 4A0666D8-F248-11E8-B48F-1D18A9856A87
last_name: Hausel
citation:
ama: 'Etesi G, Hausel T. Geometric construction of new Yang-Mills instantons over
Taub-NUT space. *Physics Letters, Section B: Nuclear, Elementary Particle and
High-Energy Physics*. 2001;514(1-2):189-199. doi:10.1016/S0370-2693(01)00821-8'
apa: 'Etesi, G., & Hausel, T. (2001). Geometric construction of new Yang-Mills
instantons over Taub-NUT space. *Physics Letters, Section B: Nuclear, Elementary
Particle and High-Energy Physics*. Elsevier. https://doi.org/10.1016/S0370-2693(01)00821-8'
chicago: 'Etesi, Gábor, and Tamás Hausel. “Geometric Construction of New Yang-Mills
Instantons over Taub-NUT Space.” *Physics Letters, Section B: Nuclear, Elementary
Particle and High-Energy Physics*. Elsevier, 2001. https://doi.org/10.1016/S0370-2693(01)00821-8.'
ieee: 'G. Etesi and T. Hausel, “Geometric construction of new Yang-Mills instantons
over Taub-NUT space,” *Physics Letters, Section B: Nuclear, Elementary Particle
and High-Energy Physics*, vol. 514, no. 1–2. Elsevier, pp. 189–199, 2001.'
ista: 'Etesi G, Hausel T. 2001. Geometric construction of new Yang-Mills instantons
over Taub-NUT space. Physics Letters, Section B: Nuclear, Elementary Particle
and High-Energy Physics. 514(1–2), 189–199.'
mla: 'Etesi, Gábor, and Tamás Hausel. “Geometric Construction of New Yang-Mills
Instantons over Taub-NUT Space.” *Physics Letters, Section B: Nuclear, Elementary
Particle and High-Energy Physics*, vol. 514, no. 1–2, Elsevier, 2001, pp. 189–99,
doi:10.1016/S0370-2693(01)00821-8.'
short: 'G. Etesi, T. Hausel, Physics Letters, Section B: Nuclear, Elementary Particle
and High-Energy Physics 514 (2001) 189–199.'
date_created: 2018-12-11T11:52:07Z
date_published: 2001-08-09T00:00:00Z
date_updated: 2021-01-12T06:50:51Z
day: '09'
doi: 10.1016/S0370-2693(01)00821-8
extern: 1
intvolume: ' 514'
issue: 1-2
main_file_link:
- open_access: '1'
url: http://arxiv.org/abs/hep-th/0105118
month: '08'
oa: 1
page: 189 - 199
publication: 'Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy
Physics'
publication_status: published
publisher: Elsevier
publist_id: '5743'
quality_controlled: 0
status: public
title: Geometric construction of new Yang-Mills instantons over Taub-NUT space
type: journal_article
volume: 514
year: '2001'
...
---
_id: '1454'
abstract:
- lang: eng
text: We address the problem of finding Abelian instantons of finite energy on the
Euclidean Schwarzschild manifold. This amounts to construct self-dual L2 harmonic
2-forms on the space. Gibbons found a non-topological L2 harmonic form in the
Taub-NUT metric, leading to Abelian instantons with continuous energy. We imitate
his construction in the case of the Euclidean Schwarzschild manifold and find
a non-topological self-dual L2 harmonic 2-form on it. We show how this gives rise
to Abelian instantons and identify them with SU(2)-instantons of Pontryagin number
2n2 found by Charap and Duff in 1977. Using results of Dodziuk and Hitchin we
also calculate the full L2 harmonic space for the Euclidean Schwarzschild manifold.
author:
- first_name: Gábor
full_name: Etesi, Gábor
last_name: Etesi
- first_name: Tamas
full_name: Tamas Hausel
id: 4A0666D8-F248-11E8-B48F-1D18A9856A87
last_name: Hausel
citation:
ama: Etesi G, Hausel T. Geometric interpretation of Schwarzschild instantons. *Journal
of Geometry and Physics*. 2001;37(1-2):126-136. doi:10.1016/S0393-0440(00)00040-1
apa: Etesi, G., & Hausel, T. (2001). Geometric interpretation of Schwarzschild
instantons. *Journal of Geometry and Physics*. Elsevier. https://doi.org/10.1016/S0393-0440(00)00040-1
chicago: Etesi, Gábor, and Tamás Hausel. “Geometric Interpretation of Schwarzschild
Instantons.” *Journal of Geometry and Physics*. Elsevier, 2001. https://doi.org/10.1016/S0393-0440(00)00040-1.
ieee: G. Etesi and T. Hausel, “Geometric interpretation of Schwarzschild instantons,”
*Journal of Geometry and Physics*, vol. 37, no. 1–2. Elsevier, pp. 126–136,
2001.
ista: Etesi G, Hausel T. 2001. Geometric interpretation of Schwarzschild instantons.
Journal of Geometry and Physics. 37(1–2), 126–136.
mla: Etesi, Gábor, and Tamás Hausel. “Geometric Interpretation of Schwarzschild
Instantons.” *Journal of Geometry and Physics*, vol. 37, no. 1–2, Elsevier,
2001, pp. 126–36, doi:10.1016/S0393-0440(00)00040-1.
short: G. Etesi, T. Hausel, Journal of Geometry and Physics 37 (2001) 126–136.
date_created: 2018-12-11T11:52:07Z
date_published: 2001-01-01T00:00:00Z
date_updated: 2021-01-12T06:50:51Z
day: '01'
doi: 10.1016/S0393-0440(00)00040-1
extern: 1
intvolume: ' 37'
issue: 1-2
main_file_link:
- open_access: '1'
url: http://arxiv.org/abs/hep-th/0003239
month: '01'
oa: 1
page: 126 - 136
publication: Journal of Geometry and Physics
publication_status: published
publisher: Elsevier
publist_id: '5744'
quality_controlled: 0
status: public
title: Geometric interpretation of Schwarzschild instantons
type: journal_article
volume: 37
year: '2001'
...
---
_id: '2340'
abstract:
- lang: eng
text: |2
Recent experimental breakthroughs in the treatment of dilute Bose gases have renewed interest in their quantum mechanical description, respectively in approximations to it. The ground state properties of dilute Bose gases confined in external potentials and interacting via repulsive short range forces are usually described by means of the Gross-Pitaevskii energy functional. In joint work with Elliott H. Lieb and Jakob Yngvason its status as an approximation for the quantum mechanical many-body ground state problem has recently been rigorously clarified. We present a summary of this work, for both the two-and three-dimensional case.
alternative_title:
- 'Operator Theory: Advances and Applications'
author:
- first_name: Robert
full_name: Robert Seiringer
id: 4AFD0470-F248-11E8-B48F-1D18A9856A87
last_name: Seiringer
orcid: 0000-0002-6781-0521
citation:
ama: 'Seiringer R. Bosons in a trap: Asymptotic exactness of the Gross-Pitaevskii
ground state energy formula. In: Demuth M, Schultze B, eds. Vol 126. Birkhäuser;
2001:307-314. doi:10.1007/978-3-0348-8231-6'
apa: 'Seiringer, R. (2001). Bosons in a trap: Asymptotic exactness of the Gross-Pitaevskii
ground state energy formula. In M. Demuth & B. Schultze (Eds.) (Vol. 126,
pp. 307–314). Presented at the PDE: Partial Differential Equations and Spectral
Theory, Birkhäuser. https://doi.org/10.1007/978-3-0348-8231-6'
chicago: 'Seiringer, Robert. “Bosons in a Trap: Asymptotic Exactness of the Gross-Pitaevskii
Ground State Energy Formula.” edited by Michael Demuth and Bert Schultze, 126:307–14.
Birkhäuser, 2001. https://doi.org/10.1007/978-3-0348-8231-6.'
ieee: 'R. Seiringer, “Bosons in a trap: Asymptotic exactness of the Gross-Pitaevskii
ground state energy formula,” presented at the PDE: Partial Differential Equations
and Spectral Theory, 2001, vol. 126, pp. 307–314.'
ista: 'Seiringer R. 2001. Bosons in a trap: Asymptotic exactness of the Gross-Pitaevskii
ground state energy formula. PDE: Partial Differential Equations and Spectral
Theory, Operator Theory: Advances and Applications, vol. 126, 307–314.'
mla: 'Seiringer, Robert. *Bosons in a Trap: Asymptotic Exactness of the Gross-Pitaevskii
Ground State Energy Formula*. Edited by Michael Demuth and Bert Schultze, vol.
126, Birkhäuser, 2001, pp. 307–14, doi:10.1007/978-3-0348-8231-6.'
short: R. Seiringer, in:, M. Demuth, B. Schultze (Eds.), Birkhäuser, 2001, pp. 307–314.
conference:
name: 'PDE: Partial Differential Equations and Spectral Theory'
date_created: 2018-12-11T11:57:05Z
date_published: 2001-01-01T00:00:00Z
date_updated: 2021-01-12T06:56:53Z
day: '01'
doi: 10.1007/978-3-0348-8231-6
editor:
- first_name: Michael
full_name: Demuth, Michael
last_name: Demuth
- first_name: Bert
full_name: Schultze, Bert-Wolfgang
last_name: Schultze
extern: 1
intvolume: ' 126'
main_file_link:
- open_access: '1'
url: http://arxiv.org/abs/math-ph/0010006
month: '01'
oa: 1
page: 307 - 314
publication_status: published
publisher: Birkhäuser
publist_id: '4586'
quality_controlled: 0
status: public
title: 'Bosons in a trap: Asymptotic exactness of the Gross-Pitaevskii ground state
energy formula'
type: conference
volume: 126
year: '2001'
...
---
_id: '2341'
abstract:
- lang: eng
text: We study the ground state properties of an atom with nuclear charge Z and
N bosonic "electrons" in the presence of a homogeneous magnetic field
B. We investigate the mean field limit N→∞ with N / Z fixed, and identify three
different asymptotic regions, according to B≪Z2,B∼Z2,andB≫Z2 . In Region 1 standard
Hartree theory is applicable. Region 3 is described by a one-dimensional functional,
which is identical to the so-called Hyper-Strong functional introduced by Lieb,
Solovej and Yngvason for atoms with fermionic electrons in the region B≫Z3 ; i.e.,
for very strong magnetic fields the ground state properties of atoms are independent
of statistics. For Region 2 we introduce a general magnetic Hartree functional,
which is studied in detail. It is shown that in the special case of an atom it
can be restricted to the subspace of zero angular momentum parallel to the magnetic
field, which simplifies the theory considerably. The functional reproduces the
energy and the one-particle reduced density matrix for the full N-particle ground
state to leading order in N, and it implies the description of the other regions
as limiting cases.
author:
- first_name: Bernhard
full_name: Baumgartner, Bernhard
last_name: Baumgartner
- first_name: Robert
full_name: Robert Seiringer
id: 4AFD0470-F248-11E8-B48F-1D18A9856A87
last_name: Seiringer
orcid: 0000-0002-6781-0521
citation:
ama: Baumgartner B, Seiringer R. Atoms with bosonic "electrons"
in strong magnetic fields. *Annales Henri Poincare*. 2001;2(1):41-76. doi:10.1007/PL00001032
apa: Baumgartner, B., & Seiringer, R. (2001). Atoms with bosonic "electrons"
in strong magnetic fields. *Annales Henri Poincare*. Birkhäuser. https://doi.org/10.1007/PL00001032
chicago: Baumgartner, Bernhard, and Robert Seiringer. “Atoms with Bosonic "Electrons"
in Strong Magnetic Fields.” *Annales Henri Poincare*. Birkhäuser, 2001. https://doi.org/10.1007/PL00001032.
ieee: B. Baumgartner and R. Seiringer, “Atoms with bosonic "electrons"
in strong magnetic fields,” *Annales Henri Poincare*, vol. 2, no. 1. Birkhäuser,
pp. 41–76, 2001.
ista: Baumgartner B, Seiringer R. 2001. Atoms with bosonic "electrons"
in strong magnetic fields. Annales Henri Poincare. 2(1), 41–76.
mla: Baumgartner, Bernhard, and Robert Seiringer. “Atoms with Bosonic "Electrons"
in Strong Magnetic Fields.” *Annales Henri Poincare*, vol. 2, no. 1, Birkhäuser,
2001, pp. 41–76, doi:10.1007/PL00001032.
short: B. Baumgartner, R. Seiringer, Annales Henri Poincare 2 (2001) 41–76.
date_created: 2018-12-11T11:57:06Z
date_published: 2001-02-01T00:00:00Z
date_updated: 2021-01-12T06:56:54Z
day: '01'
doi: 10.1007/PL00001032
extern: 1
intvolume: ' 2'
issue: '1'
main_file_link:
- open_access: '1'
url: http://arxiv.org/abs/math-ph/0007007
month: '02'
oa: 1
page: 41 - 76
publication: Annales Henri Poincare
publication_status: published
publisher: Birkhäuser
publist_id: '4585'
quality_controlled: 0
status: public
title: Atoms with bosonic "electrons" in strong magnetic fields
type: journal_article
volume: 2
year: '2001'
...