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Bound-state solutions of the Maxwell-Dirac and the Klein-Gordon-Dirac systems

✍ Scribed by Maria J. Esteban; Vladimir Georgiev; Eric Séré

Publisher
Springer
Year
1996
Tongue
English
Weight
195 KB
Volume
38
Category
Article
ISSN
0377-9017

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✦ Synopsis

In this Letter we present a result conceming the existence of stationary solutions for the classical Maxwell-Dirac equations in the Lorentz gauge. We believe that such a result can be of interest for a field quantization approach in QED. This result is obtained by using variational arguments. By a similar method, we also find an infinity of distinct solutions for the Klein-Gordon-Dirac system, arising in the so-called Yukawa model.

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## Communicated by R. Racke We prove the existence of the wave operator for the system of the massive Dirac-Klein-Gordon equations in three space dimensions where the masses m, M>0. We prove that for the small final data w + ∈ (H 3 2 +l,1 ) 4 , (/ + 1 , / + 2 ) ∈ H 2+l,1 ×H 1+l,1 , with l = 5 4 -