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Multi-time Integral Eqs.

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Interacting relativistic quantum dynamics via multi time integral equations

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 manif... ver más

31/05/2019

240K€

Presupuesto del proyecto: 240K€

Líder del proyecto

EBERHARD KARLS UNIVERSITAET TUEBINGEN No se ha especificado una descripción o un objeto social para esta compañía.

TRL 4-5

Fecha límite participación Sin fecha límite de participación.

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Financiación concedida El organismo H2020 notifico la concesión del proyecto el día 2019-05-31

MSCA-IF-2015-GF: Marie Skłodowska-Curie Individual F...

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3 Participantes

239.86K€ | Lider

RUTGERS, THE STATE UNIVERSIT...

RUTGERS

160.13K€ | Participante

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Duración del proyecto: 38 meses Fecha Inicio: 2016-03-04
Fecha Fin: 2019-05-31

Líder del proyecto

EBERHARD KARLS UNIVERSITAET TUEBINGEN No se ha especificado una descripción o un objeto social para esta compañía.

TRL 4-5

Presupuesto del proyecto 240K€

Fecha límite de participación Sin fecha límite de participación.

Descripción del proyecto 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.

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