---
_id: '2350'
abstract:
- lang: eng
text: Using the Pauli-Fierz model of non-relativistic quantum electrodynamics, we
calculate the binding energy of an electron in the field of a nucleus of charge
Z and in presence of the quantized radiation field. We consider the case of small
coupling constant α, but fixed Zα and ultraviolet cut-off Λ. We prove that after
renormalizing the mass the binding energy has, to leading order in α, a finite
limit as Λ goes to infinity; i.e., the cut-off can be removed. The expression
for the ground state energy shift thus obtained agrees with Bethe's formula for
small values of Zα, but shows a different behavior for bigger values.
acknowledgement: "We are grateful to Elliott Lieb for helpful discussions. C.H. was
supported by a Marie Curie Fellowship of the European Community programme “Improving
Human Research Potential and the Socioeconomic Knowledge Base” under contract number
HPMFCT-2000-00660 and by the Deutsche Forschungsgemeinschaft, and acknowledges kind
hospitality at Princeton University, where part of this work was done. R.S. was
supported by the Austrian Science Fund in the form of an Erwin Schrödinger Fellowship.\r\n"
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Christian
full_name: Hainzl, Christian
last_name: Hainzl
- first_name: Robert
full_name: Seiringer, Robert
id: 4AFD0470-F248-11E8-B48F-1D18A9856A87
last_name: Seiringer
orcid: 0000-0002-6781-0521
citation:
ama: Hainzl C, Seiringer R. Mass renormalization and energy level shift in non-relativistic
QED. Advances in Theoretical and Mathematical Physics. 2002;6(5):847-871.
doi:10.4310/ATMP.2002.v6.n5.a3
apa: Hainzl, C., & Seiringer, R. (2002). Mass renormalization and energy level
shift in non-relativistic QED. Advances in Theoretical and Mathematical Physics.
International Press. https://doi.org/10.4310/ATMP.2002.v6.n5.a3
chicago: Hainzl, Christian, and Robert Seiringer. “Mass Renormalization and Energy
Level Shift in Non-Relativistic QED.” Advances in Theoretical and Mathematical
Physics. International Press, 2002. https://doi.org/10.4310/ATMP.2002.v6.n5.a3.
ieee: C. Hainzl and R. Seiringer, “Mass renormalization and energy level shift in
non-relativistic QED,” Advances in Theoretical and Mathematical Physics,
vol. 6, no. 5. International Press, pp. 847–871, 2002.
ista: Hainzl C, Seiringer R. 2002. Mass renormalization and energy level shift in
non-relativistic QED. Advances in Theoretical and Mathematical Physics. 6(5),
847–871.
mla: Hainzl, Christian, and Robert Seiringer. “Mass Renormalization and Energy Level
Shift in Non-Relativistic QED.” Advances in Theoretical and Mathematical Physics,
vol. 6, no. 5, International Press, 2002, pp. 847–71, doi:10.4310/ATMP.2002.v6.n5.a3.
short: C. Hainzl, R. Seiringer, Advances in Theoretical and Mathematical Physics
6 (2002) 847–871.
date_created: 2018-12-11T11:57:09Z
date_published: 2002-09-01T00:00:00Z
date_updated: 2023-07-26T08:29:28Z
day: '01'
doi: 10.4310/ATMP.2002.v6.n5.a3
extern: '1'
external_id:
arxiv:
- math-ph/0205044v3
intvolume: ' 6'
issue: '5'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: http://arxiv.org/abs/math-ph/0205044
month: '09'
oa: 1
oa_version: Published Version
page: 847 - 871
publication: Advances in Theoretical and Mathematical Physics
publication_identifier:
issn:
- 1095-0761
publication_status: published
publisher: International Press
publist_id: '4574'
quality_controlled: '1'
scopus_import: '1'
status: public
title: Mass renormalization and energy level shift in non-relativistic QED
type: journal_article
user_id: ea97e931-d5af-11eb-85d4-e6957dddbf17
volume: 6
year: '2002'
...
---
_id: '2736'
abstract:
- lang: eng
text: We consider the time evolution of N bosonic particles interacting via a mean
field Coulomb potential. Suppose the initial state is a product wavefunction.
We show that at any finite time the correlation functions factorize in the limit
N → ∞. Furthermore, the limiting one particle density matrix satisfies the nonlinear
Hartree equation. The key ingredients are the uniqueness of the BBGKY hierarchy
for the correlation functions and a new apriori estimate for the many-body Schrödinger
equations.
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: Horng
full_name: Yau, Horng
last_name: Yau
citation:
ama: Erdös L, Yau H. Derivation of the nonlinear Schrödinger equation from a many
body Coulomb system. Advances in Theoretical and Mathematical Physics.
2001;5(6):1169-1205. doi:10.48550/arXiv.math-ph/0111042
apa: Erdös, L., & Yau, H. (2001). Derivation of the nonlinear Schrödinger equation
from a many body Coulomb system. Advances in Theoretical and Mathematical Physics.
International Press. https://doi.org/10.48550/arXiv.math-ph/0111042
chicago: Erdös, László, and Horng Yau. “Derivation of the Nonlinear Schrödinger
Equation from a Many Body Coulomb System.” Advances in Theoretical and Mathematical
Physics. International Press, 2001. https://doi.org/10.48550/arXiv.math-ph/0111042.
ieee: L. Erdös and H. Yau, “Derivation of the nonlinear Schrödinger equation from
a many body Coulomb system,” Advances in Theoretical and Mathematical Physics,
vol. 5, no. 6. International Press, pp. 1169–1205, 2001.
ista: Erdös L, Yau H. 2001. Derivation of the nonlinear Schrödinger equation from
a many body Coulomb system. Advances in Theoretical and Mathematical Physics.
5(6), 1169–1205.
mla: Erdös, László, and Horng Yau. “Derivation of the Nonlinear Schrödinger Equation
from a Many Body Coulomb System.” Advances in Theoretical and Mathematical
Physics, vol. 5, no. 6, International Press, 2001, pp. 1169–205, doi:10.48550/arXiv.math-ph/0111042.
short: L. Erdös, H. Yau, Advances in Theoretical and Mathematical Physics 5 (2001)
1169–1205.
date_created: 2018-12-11T11:59:20Z
date_published: 2001-11-01T00:00:00Z
date_updated: 2023-05-16T12:12:41Z
day: '01'
doi: 10.48550/arXiv.math-ph/0111042
extern: '1'
external_id:
arxiv:
- math-ph/0111042
intvolume: ' 5'
issue: '6'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: http://arxiv.org/abs/math-ph/0111042
month: '11'
oa: 1
oa_version: Published Version
page: 1169 - 1205
publication: Advances in Theoretical and Mathematical Physics
publication_identifier:
issn:
- 1095-0761
publication_status: published
publisher: International Press
publist_id: '4156'
quality_controlled: '1'
scopus_import: '1'
status: public
title: Derivation of the nonlinear Schrödinger equation from a many body Coulomb system
type: journal_article
user_id: ea97e931-d5af-11eb-85d4-e6957dddbf17
volume: 5
year: '2001'
...
---
_id: '1450'
abstract:
- lang: eng
text: In this paper we consider the topological side of a problem which is the analogue
of Sen's S-duality testing conjecture for Hitchin's moduli space M of rank 2 stable
Higgs bundles of fixed determinant of odd degree over a Riemann surface ∑. We
prove that all intersection numbers in the compactly supported cohomology of M
vanish, i.e. "there are no topological L2 harmonic forms on M". This
result generalizes the well known vanishing of the Euler characteristic of the
moduli space of rank 2 stable bundles N of fixed determinant of odd degree over
∑. Our proof shows that the vanishing of all intersection numbers of H* cpt(M)
is given by relations analogous to the Mumford relations in the cohomology ring
of N.
acknowledgement: "First of all I would like to thank my supervisor Nigel Hitchin for
suggesting Problem 1, and for his help and \r\n encouragement. I am grateful to
Michael Thaddeus for his inspiring paper [Thai], enlightening communications and
his constant interest in my work. I am also indebted to Manfred Lehn for the idea
of the proof of Theorem 6.2. I have found\r\nconversations with Michael Atiyah,
Frances Kirwan and Graeme Segal very stimulating. I thank the Mathematical Institute
and St. Catherine's College, Oxford for their hospitality during the preparation
of this work. Finally I thank Trinity College, Cambridge for financial support."
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Tamas
full_name: Hausel, Tamas
id: 4A0666D8-F248-11E8-B48F-1D18A9856A87
last_name: Hausel
citation:
ama: Hausel T. Vanishing of intersection numbers on the moduli space of Higgs bundles.
Advances in Theoretical and Mathematical Physics. 1998;2(5):1011-1040.
doi:10.4310/ATMP.1998.v2.n5.a3
apa: Hausel, T. (1998). Vanishing of intersection numbers on the moduli space of
Higgs bundles. Advances in Theoretical and Mathematical Physics. International
Press. https://doi.org/10.4310/ATMP.1998.v2.n5.a3
chicago: Hausel, Tamás. “Vanishing of Intersection Numbers on the Moduli Space of
Higgs Bundles.” Advances in Theoretical and Mathematical Physics. International
Press, 1998. https://doi.org/10.4310/ATMP.1998.v2.n5.a3.
ieee: T. Hausel, “Vanishing of intersection numbers on the moduli space of Higgs
bundles,” Advances in Theoretical and Mathematical Physics, vol. 2, no.
5. International Press, pp. 1011–1040, 1998.
ista: Hausel T. 1998. Vanishing of intersection numbers on the moduli space of Higgs
bundles. Advances in Theoretical and Mathematical Physics. 2(5), 1011–1040.
mla: Hausel, Tamás. “Vanishing of Intersection Numbers on the Moduli Space of Higgs
Bundles.” Advances in Theoretical and Mathematical Physics, vol. 2, no.
5, International Press, 1998, pp. 1011–40, doi:10.4310/ATMP.1998.v2.n5.a3.
short: T. Hausel, Advances in Theoretical and Mathematical Physics 2 (1998) 1011–1040.
date_created: 2018-12-11T11:52:06Z
date_published: 1998-09-01T00:00:00Z
date_updated: 2022-09-01T14:09:49Z
day: '01'
doi: 10.4310/ATMP.1998.v2.n5.a3
extern: '1'
external_id:
arxiv:
- math/9805071
intvolume: ' 2'
issue: '5'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: http://arxiv.org/abs/math/9805071
month: '09'
oa: 1
oa_version: Preprint
page: 1011 - 1040
publication: Advances in Theoretical and Mathematical Physics
publication_identifier:
issn:
- 1095-0761
publication_status: published
publisher: International Press
publist_id: '5747'
quality_controlled: '1'
scopus_import: '1'
status: public
title: Vanishing of intersection numbers on the moduli space of Higgs bundles
type: journal_article
user_id: ea97e931-d5af-11eb-85d4-e6957dddbf17
volume: 2
year: '1998'
...