Multi-time wave functions are quantum-mechanical wave functions with N space-time arguments for N particles. They were suggested by the Nobel laureates Dirac, Tomonaga and Schwinger as a particularly natural way of achieving manifest Lorentz invariance in the Schrödinger picture. While for a long time it was not clear how to obtain consistent interacting dynamics for multi-time wave functions, this has changed recently when a series of papers has clarified the theory of multi-time Schrödinger equations and provided the first interacting toy models. This project aims, with the long-term goal of a rigorous multi-time formulation of quantum field theory in mind, at improving on these models by considering the possibility of integral equations to formulate interacting dynamics for multi-time wave functions of N=2 particles. This is especially promising, as integral equations avoid a restrictive consistency condition that one faces for differential multi-time equations. Furthermore, the typical ultraviolet divergencies of quantum field theory are avoided. The objectives are (1) to study the existence of solutions of a particular integral equation similar to the Bethe-Salpeter equation, (2) to assess whether the integral equation is compatible with a probabilistic meaning, as well as (3) to determine the classical limit of the integral equation and to compare it with the action-at-a-distance formulation of classical electrodynamics due to Gauß, Fokker, Tetrode, Wheeler and Feynman. Objective (1) shall be approached using the theory of Fredholm integral equations, as well as partial results in the physics literature. For (2), suitable conserved tensor currents with a positive density component shall be constructed. (3) shall be reached by studying wave packets concentrated around the classical world-lines of particles using (and extending) functional-analytic methods of the classical limit, such as Hagedorn wave packets and Wigner functions.

Enzymatically active RNA-guided proteins, like the RNA-induced silencing complex (RISC), are particularly versatile tools for the rationally programmed manipulation of genetic information. After successful re-addressing of various natural RNA-guided machineries it is now time to tackle the engineering of novel, user-defined tools. With this respect we have recently achieved the engineering of an RNA-guided adenosine-to-inosine RNA editing machinery. Since inosine is biochemically read as guanosine, A-to-I editing alters genomic information on the RNA-level and may potentially allow for the manipulation of RNA processing or protein function. We have already achieved to apply our RNA editing approach for the repair of several missense and nonsense point mutations on reporter and disease-related genes in vitro and demonstrated its applicability in mammalian cell culture. Now, we want to push the method further towards application. To enable editing in oocytes, primary cells and neurons, we will establish to deliver the editing tool by lentiviral vectors and stabilized mRNAs. We further aim to create cell lines expressing the artificial editing machinery under conditional control. We will repair reporter genes in developing worm oocytes, and we want to reconstitute mutations that cause neuro-diseases. We also wish to establish new features including photocontrol and the application of editing to steer protein localization. If successful, site-directed RNA editing will enable us to manipulate RNA and protein function in a yet unprecedented way. The ready introduction of point mutations into mRNAs without the need for genomic engineering may dramatically facilitate the study of protein function, disease mechanism and may even allow for the treatment of diseases based on personalized genetic information.