About Me

Currently, I am a postdoc at the Mathematics Department of Tübingen from June 2018 - May 2019, within the scope of a Marie Curie Global Individual Fellowship of the European Union, hosted by Stefan Teufel and Roderich Tumulka.
My main research topic are multi-time wave functions (quantum-mechanical wave functions with many space-time arguments), in particular to consider integral equations as time evolution equations for these wave functions (see "Current Research Project").
I obtained my PhD in Mathematics at the University of Munich in Detlef Dürr's group, my Master in Theoretical Physics at the University of Cambridge and my Bachelor in Physics at the University of Göttingen.

Contact

Mailing Address:
Universität Tübingen
Fachbereich Mathematik
AB Mathematische Physik
Auf der Morgenstelle 10
72076 Tübingen
Germany
Room No.: C4 A45
Phone: +49 (0)7071 29 78696
Email: matthias.lienert[at]uni-tuebingen.de

Current Research Project

Marie Curie Action "Interacting Relativistic Quantum Dynamics via Multi-Time Integral Equations" (June 2016 - May 2019)

Multi-time wave functions are quantum-mechanical wave functions with N space-time arguments for N particles. They are needed in relativistic quantum mechanics to obtain a relativistic generalization of the Schrödinger picture, exchanging configuration 3-space with configuration space-time. Because of the many time coordinates the structure of time evolution equations changes, and this has proven a major challenge for finding interacting evolution equations. (See here for a review.)
In this project, integral equations shall be studied as a possible mechanism of interaction for multi-time wave functions. (One possibility for two electromagnetically interacting Dirac particles is shown in the photo at the top.) In this case, the multi-time evolution equations take an action-at-a-distance form with fields extracted solely from the respective other particle's degrees of freedom. This leads to the hope that one might thereby avoid the self-interaction problem in a similar way as in the Wheeler-Feynman formulation of classical electrodynamics.

The main goals are:

This project has received funding from the European Union's Framework for Research and Innovation "Horizon 2020" (2014-2020) under the Marie Sklodowska-Curie Grant Agreement No. 705295.

General Research Interests

Summer School on Paradoxes in Quantum Physics (September 2-6, 2019)

Website

Spring School on Multi-Time Wave Functions (April 10-12, 2019)

Website

Workshop on Multi-Time Wave Functions (March 26-27, 2018)

Website

Publications

My papers on arXiv

Teaching

University of Tübingen
Rutgers University, USA
University of Munich (LMU)