Seminar: Dirac Sea in QED
Organizers: D.-A. Deckert, F. Merkl
Space-Times: Every Wed 10-12, HS B 134
Abstract
The central topic of this seminar is the mathematical description of the Dirac sea in Quantum Electrodynamics. It was introduced by P.A.M. Dirac in 1933 and serves to describe electron-positron pair-creation. In quantum electrodynamics, computations are usually carried out by formal application of perturbation theory. The resulting series expansions are equally formal, and furthermore, carry divergences which have to be sorted out by hand. The hope is always that the first few of the remaining summands already provide sufficient predictive power in certain regimes. Such recipes have very successfully applied in high energy physics. However, more and more experiments come in technological reach where such recipes are likely to fail, and a non-perturbative description has to be developed. We will discuss a range of topics from the classical literature to recent developments in Theoretical Physics and Mathematical Physics. Particular emphasis will be on the current research on the topic of the time evolution of the Dirac sea in external fields and the geometric phase of QED.
Topics, Dates, and scheduled Speakers
- [22.10.14 by D. Mitrouskas] Fock Spaces, Implementation of One-Particle Operators, Formulation of Shale-Stinespring Criterion.
- [29.10.14 by D. Mitrouskas] Fock Spaces, Implementation of One-Particle Operators, Formulation of Shale-Stinespring Criterion.
- [05.11.14 by M. Noeth] Ruijsenaars Criterion.
- [12.11.14 by M. Jeblick] Wedge Spaces I: Polarization classes and excitations of the Dirac sea.
- [19.11.14 by M. Jeblick] Last talk continued.
- [26.11.14 cancled]
- [05.11.14 by M. Jeblick] Wedge Spaces I: Polarization classes and excitations of the Dirac sea.
- [03.12.14 by J. Nissen-Meyer] Wedge Spaces II: Left and Right Operations, Shale-Stinespring Criterion revisited.
- [03.12.14 by P. Reichert ] Wedge Spaces III: Shale-Stinespring Theorem
- [10.12.14 by M. Oelker] Implementation of the time evolution on time-varying Fock space.
- [07.01.15 by F. Merkl] Compact, Trace Class, and Hilbert-Schmidt Operators I.
- [14.01.15 by F. Merkl] Compact, Trace Class, and Hilbert-Schmidt Operators II.
Literature
- Dirac. "Théorie du positron." Solvay report 25 (1934): 203-212. (or in Selected Papers on QED" edited by Schwinger)
- Dirac. "The principles of quantum mechanics." (1930).
- Dyson. "1951 Lectures on Advanced Quantum Mechanics Second Edition." arXiv preprint quant-ph/0608140 (2006).
- Deckert, Dürr, Merkl, Schottenloher. "Time evolution of the external field problem in QED." arXiv preprint arXiv:0906.0046 (2009).
- Scharf. "Finite quantum electrodynamics." Berlin: Springer-Verlag, 1989.
- Thaller. "The dirac equation." Vol. 31. Berlin: Springer-Verlag, 1992.
- Lazarovivi. "The Geometric Phase in QED." http://www.mathematik.uni-muenchen.de/~bohmmech/theses/Lazarovici_Dustin_Dipl.pdf
- Pressley, Segal. "Loop groups." Clarendon Press, 1986.