# Theory Seminar: Multi-Time formalism in a Quantum Field Theory Model

Sascha Lill

In order to describe a Quantum-N -body system in the Schrödinger picture in a manifestly covariant way, one needs to introduce a separate time coordinate t k for each of the particles k∈{1, …, N}

Sascha Lill

Special theory group seminar at 11:30 am in the theory group seminar room B2.46

Thu 11. July 2019, 11:30 am

Abstract:

In order to describe a Quantum-N -body system in the Schrödinger picture in a manifestly covariant way, one needs to introduce a separate time coordinate t k for each of the particles k∈{1, …, N}. The wave function therefore depends on N time coordinates (“Multi-Time wave function”) and the Schrödinger equation becomes a system of N Partial Differential Equations (PDEs). Multi-Time wave functions were already introduced in the 1930’s and have become a topic of active research again throughout the past years.

So far, a series of papers has been published, which investigate the existence and uniqueness of solutions to the Multi-Time Schrödinger equation systems appearing in various quantum mechanical models. However, most of the considerations in these papers were done on a non-rigorous level, for example by checking a certain consistency condition. In my master thesis, I could establish a rigorous proof of existence and uniqueness of a solution to the equations of motion for a Quantum Field Theory (QFT) toy model. This talk will concern about Multi-Time formal- ism in general, how to construct a solution to the equations of motion and how to show that this PDE system is actually solved.