• 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}
}
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… 
View PDF on arXiv

References

SHOWING 1-10 OF 28 REFERENCES
Construction of the Pauli–Villars-Regulated Dirac Vacuum in Electromagnetic Fields
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
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
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
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…
From the Klein–Gordon–Zakharov system to the Klein–Gordon equation
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 Mean-Field Approximation in Quantum Electrodynamics. The no-photon case
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…
THE CUBIC DIRAC EQUATION : SMALL INITIAL DATA IN H 1 ( R 3 )
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…
Relativistic mean field theory in finite nuclei
Recent applications of relativistic mean field theory for finite nuclei are reviewed. We discuss the description of ground states of nuclei and their properties like nuclear radii as well as…
From quantum electrodynamics to mean-field theory. II. Variational stability of the vacuum of quantum electrodynamics in the mean-field approximation
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
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…
...
1
2
3
...