A variational study of some hadron bag models

Loïc Le Treust (1)

1 CEREMADE - CEntre de REcherches en MAthématiques de la DEcision

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.

Mots clés: Nonlinear equation; Dirac operator; Hadron bag model; Soliton bag model; Friedberg-Lee model; M.I.T. bag model; Supersymmetry; Ground and excited states; Foldy- Wouthuysen transformation; Variational method; Gamma-convergence; Gradient theory of phase transitions; Concentration compactness method; Free boundary problem

Domaines: Equations aux dérivées partielles [math.AP]; Physique mathématique [math-ph]

Loïc Le Treust. A variational study of some hadron bag models. Calculus of Variations and Partial Differential Equations, 2014. ⟨hal-00714457v2⟩