Sascha Lill received his Bachelor’s degree in Mathematics and Bachelor degree in Physisc from the Otto von Guericke University in 2016 and in 2018 he obtained a Master’s degree in Theoretical and Mathematical Physics (TMP) from the LMU Munich.
He joined the Basque Center for Applied Mathematics – BCAM as a PhD student in 2021 within Quantum Mechanics research line.
His PhD thesis, Time Dynamics in Quantum Field Theory Systems, has been supervised by Prof. Roderich Tumulka (University of Tübingen), Prof. Jean-Bernard Bru (BCAM-Ikerbasque-UPV/EHU) and Prof. Stefan Teufel (University of Tübingen).
The defense will be held online, through the platform Zoom. It will take place on Monday 27th June at 14:00, and users will be able to follow it live using the following link: https://zoom.us/j/9274418792?pwd=VGFSdVBTdlc0M0c4SGtzTzNaMTFpZz09
On behalf of all BCAM members, we would like to wish Sascha the best of luck in his upcoming thesis defense.
PhD thesis Title:
Time Dynamics in Quantum Field Theory Systems
Establishing a rigorous description of non-perturbative dynamics in quantum systems with particle creation and annihilation (here called Quantum Field Theory or QFT systems) can, depending on the model, be a considerable mathematical challenge. We discuss some novel mathematical tools which may simplify such kind of descriptions in future investigations.
One tool is an axiomatic setting called “Hypersurface Evolution” and recently introduced by Lienert and Tumulka, which serves as a Schrödinger picture alternative to the widely used Haag-Kastler setting. Using Hypersurface Evolutions, we establish a proof for Born’s rule on arbitrary Cauchy surfaces.
A further set of tools is given in the framework of Fock space extensions. We discuss applications of the Infinite Tensor Product (ITP) space construction proposed by von Neumann in the 1930s. Further, we introduce a second Fock space extension framework, called Extended State Space (ESS), which rigorously accommodates divergent sums and integrals appearing in QFT. Both settings are applied to simple physical examples involving Weyl and Bogoliubov transformations.