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.

Universität Tübingen

Fachbereich Mathematik

AB Mathematische Physik

Auf der Morgenstelle 10

72076 Tübingen

Germany

In this project,

The

- to prove the existence of solutions of multi-time integral equations,
- to classify the solution spaces (differently than by Cauchy data),
- to identify conserved quantities, currents and probability densities,
- to study the classical limit and compare it with Wheeler-Feynman-Electrodynamics.

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.

- Mathematical physics
- Relativistic quantum theory
- Foundations of quantum mechanics
- Multi-time wave equations
- Quantum field theory
- Construction of rigorous interacting relativistic models
- Attempts at "quantising" Wheeler-Feynman-Electrodynamics
- Integral equations

My papers on arXiv

- M. Lienert and M. Nöth,
*Singular light cone interactions of scalar particles in 1+3 dimensions,*arXiv:2003.08677 - M. K.-H. Kiessling, M. Lienert and A. S. Tahvildar-Zadeh,
*A Lorentz-Covariant Interacting Electron-Photon System in One Space Dimension,*arXiv:1906.03632 - M. Lienert and M. Nöth,
*Existence of relativistic dynamics for two directly interacting Dirac particles in 1+3 dimensions,*arXiv:1903.06020 - M. Lienert and L. Nickel,
*Multi-time formulation of particle creation and annihilation via interior-boundary conditions,***Rev. Math. Phys.**32, 2050004 (2020) link - M. Lienert and R. Tumulka,
*Interacting relativistic quantum dynamics of two particles on spacetimes with a Big Bang singularity,***J. Math. Phys.**60, 042302 (2019) link - M. Lienert and R. Tumulka,
*A new class of Volterra-type integral equations from relativistic quantum physics,***J. Integral Equations Applications.**31, 535-569 (2019), link - M. Lienert,
*Direct interaction along light cones at the quantum level,***J. Phys. A: Math. Theor.**51 435302 (2018) link - M. Lienert, S. Petrat, and R. Tumulka,
*Multi-time wave functions versus multiple timelike dimensions,***Found. Phys.**47, 1582-1590 (2017) link - M. Lienert and R. Tumulka,
*Born's rule for arbitrary Cauchy surfaces,***Lett. Math. Phys.**110, 753-804 (2020), link - M. Lienert, S. Petrat, and R. Tumulka,
*Multi-time wave functions,***J. Phys.: Conf. Ser.**880: 012006 (2017), link - M. Lienert,
*Interacting relativistic quantum dynamics for multi-time wave functions*,**EPJ Web of Conferences**128, 04026 (2016), link - PhD thesis:
*Lorentz invariant quantum dynamics in the multi-time formalism,*link (06/2015) - M. Lienert and L. Nickel,
*A simple explicitly solvable interacting relativistic N-particle model,*

**J. Phys. A: Math. Theor.**48, 325301 (2015), link - M. Lienert,
*On the question of current conservation for the Two-Body Dirac equations of constraint theory,*

**J. Phys. A: Math. Theor.**48, 325302 (2015), link - M. Lienert,
*A relativistically interacting exactly solvable multi-time model for two mass-less Dirac particles in 1+1 dimensions,*

**J. Math. Phys.**56, 042301 (2015), link - D. Dürr and M. Lienert,
*On the description of subsystems in relativistic hypersurface Bohmian mechanics,*

**Proc. R. Soc. A**470, 20140181 (2014), link

- Summer 2020: Lecture on Integral Theorems
- Winter 2019/20: Seminar Complex Analysis
- Summer 2019: Repetitorium Analysis 2
- Winter 2018/19: Lecture Wave Equations of Relativistic Quantum Mechanics

- Fall 2016-Spring 2018: Work in Progress Seminar in Mathematical Physics

- Winter 2015/16: Assistant for Mathematics III for Physicists (Prof. D. Dürr)
- Summer 2015: Research workshop Lehre@LMU
- Winter 2014/15: Research workshop Lehre@LMU
- Summer 2014: Seminar on number theory for high school teachers, with Prof. P. Pickl
- Winter 2013/14: Multi-dimensional Analysis (Prof. P. Pickl)
- Winter 2012/13: Seminar: Relativistic quantum mechanics (with Prof. P. Pickl)
- Summer 2012: Mentoring of student projects: Lehre@LMU
- Winter 2011/12: Mathematics III for Physicists (Prof. D. Dürr)