Matthias Lienert
Marie Curie Postdoctoral Fellow
About Me
Currently, I am a postdoc and visiting researcher at the Rutgers Department of Mathematics from June 2016 - May 2018,
within the scope of a Marie Curie Global Individual Fellowship of the European Union,
hosted by Sheldon Goldstein at Rutgers
as well as Stefan Teufel
and Roderich Tumulka at the University of Tübingen.
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:
Department of Mathematics
Rutgers University
110 Freylinghuysen Road
Piscataway, NJ 08854-8019
USA
Room No.: Hill Center 636
Phone: (+1) 848-445-56783
Email: m.lienert[at]rutgers.edu
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
Publications
My papers on arXiv- M. Lienert and R. Tumulka, Interacting relativistic quantum dynamics of two particles on spacetimes with a Big Bang singularity, arXiv:1805.006348
- M. Lienert and R. Tumulka, A new class of Volterra-type integral equations from relativistic quantum physics, arXiv:1803.08792
- M. Lienert, Direct interaction along light cones at the quantum level, arXiv:1801.00060
- 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, arXiv:1706.07074
- 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
- Spring Semester 2018: Organization of Work in Progress Seminar in Mathematical Physics
- Fall Semester 2017: Organization of "Work in Progress Seminar in Mathematical Physics"
- Spring Semester 2017: Organization of "Work in Progress Seminar in Mathematical Physics"
- Fall Semester 2016: Organization of "Work in Progress Seminar in Mathematical Physics"
- Winter Semester 2015/16: Assistant for Mathematics III for Physicists (Prof. D. Dürr)
- Summer Semester 2015: Organization of research seminar Lehre@LMU
- Winter Semester 2014/15: Organization of research seminar Lehre@LMU
- Summer Semester 2014: Seminar on number theory for high school teachers, with Prof. P. Pickl
- Winter Semester 2013/14: Multi-dimensional Analysis (Prof. P. Pickl)
- Winter Semester 2012/13: Seminar: Relativistic quantum mechanics (with Prof. P. Pickl)
- Summer Semester 2012: Mentoring of student projects: Lehre@LMU
- Winter Semester 2011/12: Mathematics III for Physicists (Prof. D. Dürr)