Self-adjointness for Dirac operators via Hardy-Dirac inequalities]{Self-adjointness of Dirac operators via Hardy-Dirac inequalities

Maria J. Esteban (1) , Michael Loss (2)

1 CEREMADE - CEntre de REcherches en MAthématiques de la DEcision
2 School of Mathematics - Georgia Institute of Technology

Distinguished selfadjoint extensions of Dirac operators are constructed for a class of potentials including Coulombic ones up to the critical case, $-|x|^{-1}$. The method uses Hardy-Dirac inequalities and quadratic form techniques.

Mots clés: Dirac operator; selfadjoint operators; selfadjointness; Dirac-Coulomb Hamiltonian; relativistic hydrogen atom; Hardy inequality; Hardy-Dirac inequality

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

Maria J. Esteban, Michael Loss. Self-adjointness for Dirac operators via Hardy-Dirac inequalities]{Self-adjointness of Dirac operators via Hardy-Dirac inequalities. Journal of Mathematical Physics, 2007, 48 (11), pp.112107. ⟨hal-00153338⟩