• Corpus ID: 239016985

# The Dirac-Klein-Gordon system in the strong coupling limit

@inproceedings{Lampart2021TheDS,
title={The Dirac-Klein-Gordon system in the strong coupling limit},
author={Jonas Lampart and Loic Le Treust and S. Rota Nodari and Julien Sabin},
year={2021}
}
• Published 18 October 2021
• Mathematics, Physics
We study the Dirac equation coupled to scalar and vector Klein-Gordon fields in the limit of strong coupling and large masses of the fields. We prove convergence of the solutions to those of a cubic non-linear Dirac equation, given that the initial spinors coincide. This shows that in this parameter regime, which is relevant to the relativistic mean-field theory of nuclei, the retarded interaction is well approximated by an instantaneous, local self-interaction. We generalize this result to a…

## References

SHOWING 1-10 OF 28 REFERENCES
Construction of the Pauli–Villars-Regulated Dirac Vacuum in Electromagnetic Fields
• Physics
• 2013
Using the Pauli–Villars regularization and arguments from convex analysis, we construct solutions to the classical time-independent Maxwell equations in Dirac’s vacuum, in the presence of small
Existence of Global-In-Time Solutions to a Generalized Dirac-Fock Type Evolution Equation
• Physics
• 2005
We consider a generalized DiracFock type evolution equation deduced from nophoton Quantum Electrodynamics, which describes the selfconsistent timeevolution of relativistic electrons, the observable
THE HARTREE EQUATION FOR INFINITELY MANY PARTICLES
• Mathematics
• 2013
We consider the nonlinear Hartree equation for an interacting gas containing infinitely many particles and we investigate the large-time stability of the stationary states of the form f(−∆),
From quantum electrodynamics to mean-field theory. I. The Bogoliubov-Dirac-Fock formalism
• Physics
• 1989
A relativistic mean-field theory for interacting Dirac particles in an external field is derived from quantum-field theory using a minimisation principle, and discussed in the context of atomic
The mean‐field approximation in quantum electrodynamics: The no‐photon case
• Physics
• 2005
We study the mean‐field approximation of quantum electrodynamics (QED) by means of a thermodynamic limit. The QED Hamiltonian is written in Coulomb gauge and does not contain any normal ordering or
From the Klein–Gordon–Zakharov system to the Klein–Gordon equation
• Mathematics
• 2016
In a singular limit, the Klein–Gordon (KG) equation can be derived from the Klein–Gordon–Zakharov (KGZ) system. We point out that for the original system posed on a d‐dimensional torus, the solutions
THE CUBIC DIRAC EQUATION : SMALL INITIAL DATA IN H 1 ( R 3 )
• Mathematics
• 2014
We establish global well-posedness and scattering for the cubic Dirac equation for small data in the critical space H(R). The main ingredient is obtaining a sharp end-point Strichartz estimate for
From quantum electrodynamics to mean-field theory. II. Variational stability of the vacuum of quantum electrodynamics in the mean-field approximation
• Physics
• 1989
For pt.I see ibid., vol.22, no.23, p.3791-814 (1989). The authors use a minimisation principle to analyse the variational stability of the translationally invariant vacuum of quantum electrodynamics,
On the dynamics of the mean-field polaron in the high-frequency limit
• Mathematics
• 2017
We consider the dynamics of the mean-field polaron in the limit of infinite phonon frequency $$\omega \rightarrow \infty$$ω→∞. This is a singular limit formally leading to a Schrödinger–Poisson