Objectif 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. Champ scientifique natural sciencesphysical sciencestheoretical physicsparticle physicsfermionsnatural sciencesphysical sciencesastronomyphysical cosmologybig bangnatural sciencesphysical sciencesquantum physicsquantum field theorynatural sciencesmathematics Programme(s) H2020-EU.1.3. - EXCELLENT SCIENCE - Marie Skłodowska-Curie Actions Main Programme H2020-EU.1.3.2. - Nurturing excellence by means of cross-border and cross-sector mobility Thème(s) MSCA-IF-2015-GF - Marie Skłodowska-Curie Individual Fellowships (IF-GF) Appel à propositions H2020-MSCA-IF-2015 Voir d’autres projets de cet appel Régime de financement MSCA-IF-GF - Global Fellowships Coordinateur EBERHARD KARLS UNIVERSITAET TUEBINGEN Contribution nette de l'UE € 239 860,80 Adresse GESCHWISTER-SCHOLL-PLATZ 72074 Tuebingen Allemagne Voir sur la carte Région Baden-Württemberg Tübingen Tübingen, Landkreis Type d’activité Higher or Secondary Education Establishments Liens Contacter l’organisation Opens in new window Site web Opens in new window Participation aux programmes de R&I de l'UE Opens in new window Réseau de collaboration HORIZON Opens in new window Coût total € 239 860,80 Partenaires (1) Trier par ordre alphabétique Trier par contribution nette de l'UE Tout développer Tout réduire Partenaire Les organisations partenaires contribuent à la mise en œuvre de l’action, mais ne signent pas la convention de subvention. RUTGERS, THE STATE UNIVERSITY OF NEW JERSEY États-Unis Contribution nette de l'UE € 0,00 Adresse RUTGERS PLAZA 3 08901 New Brunswick Voir sur la carte Type d’activité Higher or Secondary Education Establishments Liens Contacter l’organisation Opens in new window Participation aux programmes de R&I de l'UE Opens in new window Réseau de collaboration HORIZON Opens in new window Coût total € 160 130,40