# Analysis and Quantum Theory

### Ryszard Nest

University of Copenhagen, Denmark### Volker Bach

Johannes Gutenberg-Universität Mainz, Germany### Jan Dereziński

Warsaw University, Poland

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## Abstract

The MFO-Workshop~0538 \emph{Analysis and Quantum Theory}, organized by V.~Bach (U~Mainz), J.~Derezinski (U~Warsaw), and J.~P.~Solovej (U~Copenhagen), was held from September 18 through September 24, 2005. The workshop's general theme was mathematical physics, it especially focussed on

- an introduction to the Epstein-Glaser Method in quantum field theory by T.~Hurth (CERN Geneva),
- an introduction to perturbative renormalization in quantum electrodynamics by E.~Remiddi (U.~Bolgna),
- an introduction to the theory of the fractional quantum Hall effect by J.~Fr\"ohlich (ETH Z\"urich),
- a review of the use of the Witten Laplacian in classical statistical mechanics by B.~Helffer (U.~Paris-Orsay),
- a review of the Bogolubov-Dirac-Fock approximation in relativistic quantum mechanics and quantum field theory by E.~S\'er\'e (U~Paris-Dauphine).

Besides these lectures of more tutorial and overview character, several seminars on current research results were delivered; see the abstracts below. The purpose of this workshops was twofold.

- The tutorial lectures were meant to bridge the gap between theoretical physics and mathematics. For example, even the notion of what is \emph{perturbative} is different in these communities and a inexhaustive source of misunderstandings between mathematicians and physicists. Indeed, the lectures by T.~Hurth and E.~Remiddi were intended to present notions of \emph{perturbative quantum field theory} to an, in majority mathematically oriented, audience.
- The seminars on current research were meant to communicate the state of the art on more specialized topics in the mathematical description of quantum mechanics and quantum field theory.

Besides the lectures present during daytime, an evening discussion on open problems and future developments took place on September 26. This discussion was chaired by J.~Fr\"ohlich who emphazised the importance that mathematical physics addresses \emph{physically relevant} problems. This criterion in competition with the criterion of \emph{feasability of its solution} should be the guiding principles of our choice of research topics. There was a general agreement of the audience to this statement.

It is a pleasure to thank the director G.-M.~Greuel, the administrative staff, and the kitchen staff of MFO, as well as, the state of Baden-W\"urtemberg (the main source of funding of MFO), for their work which made this workshop possible.