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Multi-time Integral Eqs.

Interacting relativistic quantum dynamics via multi-time integral equations

Total Cost €


EC-Contrib. €






 Multi-time Integral Eqs. project word cloud

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Project "Multi-time Integral Eqs." data sheet

The following table provides information about the project.


Organization address
postcode: 72074

contact info
title: n.a.
name: n.a.
surname: n.a.
function: n.a.
email: n.a.
telephone: n.a.
fax: n.a.

 Coordinator Country Germany [DE]
 Project website
 Total cost 239˙860 €
 EC max contribution 239˙860 € (100%)
 Programme 1. H2020-EU.1.3.2. (Nurturing excellence by means of cross-border and cross-sector mobility)
 Code Call H2020-MSCA-IF-2015
 Funding Scheme MSCA-IF-GF
 Starting year 2016
 Duration (year-month-day) from 2016-06-01   to  2019-05-31


Take a look of project's partnership.

# participants  country  role  EC contrib. [€] 


 Project 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.


year authors and title journal last update
List of publications.
2019 Lienert, Matthias; Nöth, Markus
Existence of relativistic dynamics for two directly interacting Dirac particles in 1+3 dimensions
published pages: all, ISSN: , DOI:
n/a n/a 2020-01-20
2017 Matthias Lienert, Sören Petrat, Roderich Tumulka
Multi-time wave functions
published pages: 12006, ISSN: 1742-6588, DOI: 10.1088/1742-6596/880/1/012006
Journal of Physics: Conference Series 880 2020-01-20
2017 Matthias Lienert, Sören Petrat, Roderich Tumulka
Multi-Time Wave Functions Versus Multiple Timelike Dimensions
published pages: 1582-1590, ISSN: 0015-9018, DOI: 10.1007/s10701-017-0120-5
Foundations of Physics 47/12 2020-01-20
2019 Matthias Lienert, Lukas Nickel
Multi-time formulation of particle creation and annihilation via interior-boundary conditions
published pages: , ISSN: 0129-055X, DOI: 10.1142/s0129055x2050004x
Reviews in Mathematical Physics 2020-01-20

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