Landau-Peierls representation of QFT

Rouven Veigel 

In 1930 L. D. Landau and R. Peierls stated equations for Quantum Electrodynamics (QED) in a particle-position representation in contrast to the usually used field operator formulations in Quantum Field Theory. In the last years M. Lienert and R. Tumulka found a multi-time equation formulation of the original Landau-Peierls equations which yields a more natural and transparent representation. However, there are still a lot of open questions and problems of the formulation including an extension to Yang-Mills theory.
After a short motivation of the topic at the beginning of the presentation, we will look at the multi-time formulation of the Landau-Peierls equations for QED. Here we consider the relevant mathematical tools  to understand the equations and motivate their formulation. Finally, we repeat the procedure for an ansatz of Landau-Peierls equations for Yang-Mills theory.