The Dirac–Klein–Gordon system in the strong coupling limit
Annales Henri Lebesgue, Volume 6 (2023), pp. 541-573.


Keywords Relativistic mean-field, nuclear physics, nonlinear analysis, asymptotic analysis, highly oscillatory equations, nonlinear Dirac equation, Klein-Gordon equation


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.


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