Variational methods in relativistic quantum mechanics

Simple item page
dc.creatorEsteban, Maria J.
dc.creatorLewin, Mathieu
dc.creatorséré, Eric
dc.date2007-06-22
dc.date2008-01-08
dc.date.accessioned2026-07-07T10:12:50Z
dc.date.available2026-07-07T10:12:50Z
dc.descriptionThis review is devoted to the study of stationary solutions of linear and nonlinear equations from relativistic quantum mechanics, involving the Dirac operator. The solutions are found as critical points of an energy functional. Contrary to the Laplacian appearing in the equations of nonrelativistic quantum mechanics, the Dirac operator has a negative continuous spectrum which is not bounded from below. This has two main consequences. First, the energy functional is strongly indefinite. Second, the Euler-Lagrange equations are linear or nonlinear eigenvalue problems with eigenvalues lying in a spectral gap (between the negative and positive continuous spectra). Moreover, since we work in the space domain R^3, the Palais-Smale condition is not satisfied. For these reasons, the problems discussed in this review pose a challenge in the Calculus of Variations. The existence proofs involve sophisticated tools from nonlinear analysis and have required new variational methods which are now applied to other problems.
dc.identifierhttps://arxiv.org/abs/0706.3309
dc.identifierhttp://arxiv.org/abs/0706.3309
dc.identifierBull. Amer. Math. Soc. (N.S.) 45, 4 (2008) 535--593
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/172321
dc.subjectMathematical Physics
dc.subjectAnalysis of PDEs
dc.titleVariational methods in relativistic quantum mechanics
dc.typetext

Files

Collections

arXiv