Objective 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. Fields of science 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 Topic(s) MSCA-IF-2015-GF - Marie Skłodowska-Curie Individual Fellowships (IF-GF) Call for proposal H2020-MSCA-IF-2015 See other projects for this call Funding Scheme MSCA-IF-GF - Global Fellowships Coordinator EBERHARD KARLS UNIVERSITAET TUEBINGEN Net EU contribution € 239 860,80 Address Geschwister-scholl-platz 72074 Tuebingen Germany See on map Region Baden-Württemberg Tübingen Tübingen, Landkreis Activity type Higher or Secondary Education Establishments Links Contact the organisation Opens in new window Website Opens in new window Participation in EU R&I programmes Opens in new window HORIZON collaboration network Opens in new window Other funding € 0,00 Partners (1) Sort alphabetically Sort by Net EU contribution Expand all Collapse all Partner Partner organisations contribute to the implementation of the action, but do not sign the Grant Agreement. RUTGERS, THE STATE UNIVERSITY OF NEW JERSEY United States Net EU contribution € 0,00 Address Rutgers plaza 3 08901 New brunswick See on map Activity type Higher or Secondary Education Establishments Links Contact the organisation Opens in new window Participation in EU R&I programmes Opens in new window HORIZON collaboration network Opens in new window Other funding € 160 130,40
