[MaPhySto logo]
Centre for Mathematical Physics and Stochastics
Department of Mathematical Sciences, University of Aarhus

Funded by The Danish National Research Foundation

Summer School on

Quantum Field Theory

- from a Hamiltonian point of view

August 2-9, 2000 at Sandbjerg Manor, Denmark

The Summer School was organized by Jan Philip Solovej (Copenhagen) and Søren Fournais (MaPhySto, Aarhus) with funding from MaPhySto and the EU-network Postdoctoral training program in partial differential equations and applications in quantum mechanics (ERBFMRXCT960001).


There were the following series of lectures (3-4 hours each):

Prof. Volker Bach, Universität Mainz:
Spectral Analysis of Nonrelativistic Quantum Electrodynamics

Prof. Jan Derezinski, University of Warsaw:
Spectral analysis of simple models of Quantum Field Theory

Prof. Gian-Michele Graf, ETH Zürich:
Stability of (ultraviolet cutoff) non-relativistic QED

Prof. Jens Hoppe, Max-Planck-Institut für Gravitationsphysik, Albert-Einstein-Institut, Potsdam:
Membranes and Matrix Models

Prof. Michael Loss, Georgia Tech:
Self-energy of electrons in nonrelativistic QED

Prof. Herbert Spohn, TU München:
Dynamics of classical charges and their radiation field

The summer school commenced in the late afternoon of Wednesday 2 August and concluded with lunch on Wednesday 9 August, 2000.


The main speakers were Bach, Derezinski, Graf, Hoppe, Loss, and Spohn. They talked in the morning. A number of 30 min. talks were also scheduled for the afternoons. Here only names are listed. Titles and abstracts can be found in the Summer School booklet (see below).

Most afternoons time were left open for discussion, questions, problem sessions, or simply for studying. On the program this is marked as discussion.

		Wed	   Thur	       Fri	   Sat
		Aug 2	   Aug 3       Aug 4	   Aug 5

 8:00- 9:00		   Breakfast   Breakfast   Breakfast

 9:00- 9:50		   Spohn       Spohn	   Spohn
10:00-10:50		   Bach	       Bach	   Derezinski
11:00-11:50		   Bach	       Bach	   Derezinski

12:00-13:30		   Lunch       Lunch	   Lunch

13:30-14:00	Arrival	   Teufel      Siedentop   Griesemer
14:00-17:00	Arrival	   Discussion  Discussion  Time off
17:00-17:30	Arrival	   Tadie       Roehrl	   Time off    

18:00-20:00	Dinner	   Dinner      Banquet	   Dinner

20:00-21:00	Opening/	      
		Intro of 

		Sun	   Mon	       Tues 	   Wed		
		Aug 6	   Aug 7       Aug 8	   Aug 9

 8:00- 9:00	Breakfast  Breakfast   Breakfast   Breakfast

 9:00- 9:50	Derezinski Loss        Hoppe       Graf
10:00-10:50	Graf       Hoppe       Loss        Hoppe
11:00-11:50	Graf       Hoppe       Loss        Discussion
12:00-13:30	Lunch	   Lunch       Lunch       Lunch	

13:30-14:00	Excursion  Spitzer     Balinsky	   Departure
14:00-17:00	  from	   Discussion  Discussion  
17:00-17:30	  13-18	   Ammari      Iantchenko	

18:00-20:00	Dinner     Dinner      Dinner

20:00-21:00			       Concluding

Summer School booklet

A booklet with some additional information may be down-loaded in:
[ gzipped postscript-format | pdf-format ]

Lecture Notes; Additional References

The following lecture notes were handed out at the course:

Volker Bach:
Spectral Analysis of Nonrelativistic Quantum Electrodynamics: [ gzipped postscript | pdf ]

Elliott H. Lieb and Michael Loss
Self-energy of electrons in non-perturbative QED: [ gzipped postscript | pdf ]

Herbert Spohn
Dynamics of Charged Particles and Their Radiation Field: [ gzipped postscript | pdf ]

Additional References

G.M. Graf
Stability of matter in classical and quantized fields. Documenta Mathematica, Proceedings of the International Congress of Mathematicians, Berlin 1998.
URL: http://www.mathematik.uni-bielefeld.de/documenta/xvol-icm/11/Graf.MAN.html

L. Erdos, J.P. Solovej
The kernel of Dirac operators on $S^3$ and $R^3$.
URL: http://www.maphysto.dk/cgi-bin/w3-msql/publications/genericpublication.html?publ=181

L. Bugliaro, G.M. Graf, J. Fröhlich
Stability of quantum electrodynamics with non-relativistic matter. Phys. Rev. Lett. 77, 3494-3497 (1996).
URL: http://publish.aps.org/abstract/PRL/v77/p3494

L. Bugliaro, C. Fefferman, G.M. Graf, J. Fröhlich, J. Stubbe
A Lieb-Thirring bound for a magnetic Pauli Hamiltonian. Commun. Math. Phys. 187, 567-582 (1997).
URL: http://link.springer.de/link/service/journals/00220/bibs/7187003/71870567.htm

L. Bugliaro, G.M. Graf, C. Fefferman
A Lieb-Thirring Bound for a Magnetic Pauli Hamiltonian, II. Revista Matematica Iberoamericana 15, 593-619 (1999).
URL: http://www.ma.utexas.edu/mp_arc-bin/mpa?yn=98-161

C. Adam, B. Muratori, C. Nash
Multiple zero modes of the Dirac operator in three dimensions.
URL: http://xxx.lanl.gov/abs/hep-th/0001164

List of Participants

This document, http://www.maphysto.dk/oldpages/events/SummerMP2000/index.html, was last modified January 19, 2004. Questions or comments to the contents of this document should be directed to maphysto@maphysto.dk.