Matthias Lienert

Marie Curie Postdoctoral Fellow

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:

• 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.

General Research Interests

• 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

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

Publication list

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

Teaching

University of Tübingen

• 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

Rutgers University, USA

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

University of Munich (LMU)

• 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)