The Dirac–Klein–Gordon system in the strong coupling limit

The Dirac–Klein–Gordon system in the strong coupling limit

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...

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Bibliographic Details
Published in:Annales Henri Lebesgue Vol. 6; pp. 541 - 573
Main Authors: Lampart, Jonas, Le Treust, Loïc, Rota Nodari, Simona, Sabin, Julien
Format: Journal Article
Language:English
Published: UFR de Mathématiques - IRMAR 02-10-2023
Subjects:
Analysis of PDEs
Mathematics
Online Access:Get full text
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Summary: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 many-body Dirac-Fock equation on the space of Hilbert-Schmidt operators.
ISSN:2644-9463
2644-9463
DOI:10.5802/ahl.171