23 July - 17 August 2012
Organisers: Malcolm Brown (Cardiff), Maria J Esteban (CEREMADE), Karl Schmidt (Cardiff) and Heinz Siedentop (Munich)
Relativistic operators are used to model important physical systems which
include transport properties of graphene, and relativistic quantum field theory.
This meeting will focus on the following areas of current research interest in
such operators applied to mathematical physics.
1. For classical (one-particle) Dirac operators, current topics of interest include
the Weyl-type theory, dissolution of eigenvalues of corresponding relativistic
systems into resonances, asymptotics of the spectral function and spectral
concentration as well as the role of the mass term of Dirac operators. We
shall concentrate on the structure of the spectrum, quadratic form methods,
singularly perturbed problems, and selfadjoint extensions as well as applications
of the Dirac operator in mathematical physics and chemistry.
2. A topic of central importance to be covered by the workshop is the stability
of matter and asymptotic behaviour of the ground state energy for relativistic many-particle systems. This problem concerns the question whether the
energy of the system of particles is bounded from below and whether it is
bounded below by a constant multiple of the number of particles. Although
the problems were settled for non-relativistic quantum mechanical electrons
and nuclei, many challenges remain when relativistic considerations are included.
3. Another major topic of the workshop concerns the multi-particle operators and connections to quantum electrodynamics. A new chapter of mathematical analysis has been opened by studying the interaction of photons with fast moving (relativising) electrons, positrons, and photons. The central problem is to investigate the physically relevant minimisers of an energy functional. The mathematical challenge is to formulate and to investigate such models analytically and thereby to provide a theoretical basis for their numerical treatment.