A variational study of some hadron bag models
Le Treust, Loïc (2014), A variational study of some hadron bag models, Calculus of Variations and Partial Differential Equations, 49, 1-2, p. 753-793. http://dx.doi.org/10.1007/s00526-013-0599-3
TypeArticle accepté pour publication ou publié
External document linkhttp://hal.archives-ouvertes.fr/hal-00714457
Journal nameCalculus of Variations and Partial Differential Equations
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Author(s)Le Treust, Loïc
Abstract (EN)Quantum 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.
Subjects / KeywordsFree boundary problem; Concentration compactness method; Gradient theory of phase transitions; Gamma-convergence; Variational method; Foldy- Wouthuysen transformation; Ground and excited states; Supersymmetry; M.I.T. bag model; Friedberg-Lee model; Soliton bag model; Hadron bag model; Dirac operator; Nonlinear equation
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