SRO
23 July 2012 to 17 August 2012
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.
The Institute kindly requests that any papers published as a result of this programme’s activities are credited as such. Please acknowledge the support of the Institute in your paper using the following text:
The author(s) would like to thank the Isaac Newton Institute for Mathematical Sciences, Cambridge, for support and hospitality during the programme Spectral theory of relativistic operators, where work on this paper was undertaken. This work was supported by EPSRC grant EP/F005431/1 and EP/I016392/1.
Click here to download the programme's final scientific report
Title | Year | Programme | Publication Date |
---|---|---|---|
Ground states for a stationary mean-field model for a nucleonAuthors: M J Esteban, Simona Rota-Nodari |
2012 | SRO | 21 October 2016 |
Eigenvalue enclosures and applications to the Maxwell operatorAuthors: GR Barrenechea, Lyonell Boulton, N Boussai |
2012 | SRO | 21 October 2016 |
30 July 2012 to 3 August 2012
Wednesday 25th July 2012 | |||
---|---|---|---|
14:00 to 15:00 |
Daniel Hughes Cardiff University |
Room 1 |
Wednesday 8th August 2012 | |||
---|---|---|---|
14:00 to 15:00 |
Monika Winklmeier Universidad de los Andes |
Room 1 |
Tuesday 14th August 2012 | |||
---|---|---|---|
14:00 to 15:00 |
Jan Philip Solovej Københavns Universitet (University of Copenhagen) |
Room 1 |
Wednesday 15th August 2012 | |||
---|---|---|---|
14:00 to 15:00 |
Volker Bach Johannes Gutenberg-Universität Mainz |
Room 1 | |
15:00 to 17:30 | Room 1 |
Thursday 16th August 2012 | |||
---|---|---|---|
14:00 to 17:30 | Discussion Room |
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