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dc.contributor.authorLe Treust, Loïc
HAL ID: 6883
ORCID: 0000-0002-6587-9090
dc.subjectFree boundary problemen
dc.subjectConcentration compactness methoden
dc.subjectGradient theory of phase transitionsen
dc.subjectVariational methoden
dc.subjectFoldy- Wouthuysen transformationen
dc.subjectGround and excited statesen
dc.subjectM.I.T. bag modelen
dc.subjectFriedberg-Lee modelen
dc.subjectSoliton bag modelen
dc.subjectHadron bag modelen
dc.subjectDirac operatoren
dc.subjectNonlinear equationen
dc.titleA variational study of some hadron bag modelsen
dc.typeArticle accepté pour publication ou publié
dc.description.abstractenQuantum chromodynamics (QCD) is the theory of strong interaction and accounts for the internal structure of hadrons. Physicists introduced phe- nomenological models such as the M.I.T. bag model, the bag approximation and the soliton bag model to study the hadronic properties. We prove, in this paper, the existence of excited state solutions in the symmetric case and of a ground state solution in the non-symmetric case for the soliton bag and the bag approximation models thanks to the concentration compactness method. We show that the energy functionals of the bag approximation model are Gamma -limits of sequences of soliton bag model energy functionals for the ground and excited state problems. The pre- compactness, up to translation, of the sequence of ground state solutions associated with the soliton bag energy functionals in the non-symmetric case is obtained combining the Gamma -convergence theory and the concentration-compactness method. Finally, we give a rigorous proof of the original derivation of the M.I.T. bag equations done by Chodos, Jaffe, Johnson, Thorn and Weisskopf via a limit of bag approximation ground state solutions in the spherical case. The supersymmetry property of the Dirac operator is the key point in many of our arguments.en
dc.relation.isversionofjnlnameCalculus of Variations and Partial Differential Equations
dc.subject.ddclabelSciences connexes (physique, astrophysique)en

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