The Dirac system on the Anti-de Sitter Universe
| dc.creator | Bachelot, Alain | |
| dc.date | 2007-06-09 | |
| dc.date | 2008-02-25 | |
| dc.date.accessioned | 2026-07-07T11:56:55Z | |
| dc.date.available | 2026-07-07T11:56:55Z | |
| dc.description | We investigate the global solutions of the Dirac equation on the Anti-de-Sitter Universe. Since this space is not globally hyperbolic, the Cauchy problem is not, {\it a priori}, well-posed. Nevertheless we can prove that there exists unitary dynamics, but its uniqueness crucially depends on the ratio beween the mass $M$ of the field and the cosmological constant $Λ>0$ : it appears a critical value, $Λ/12$, which plays a role similar to the Breitenlohner-Freedman bound for the scalar fields. When $M^2\geq Λ/12$ there exists a unique unitary dynamics. In opposite, for the light fermions satisfying $M^2<Λ/12$, we construct several asymptotic conditions at infinity, such that the problem becomes well-posed. In all the cases, the spectrum of the hamiltonian is discrete. We also prove a result of equipartition of the energy. | |
| dc.description | 33 pages | |
| dc.identifier | https://arxiv.org/abs/0706.1315 | |
| dc.identifier | http://arxiv.org/abs/0706.1315 | |
| dc.identifier | Commun.Math.Phys.283:127-167,2008 | |
| dc.identifier | doi:10.1007/s00220-008-0564-8 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/205707 | |
| dc.subject | Mathematical Physics | |
| dc.subject | Analysis of PDEs | |
| dc.subject | 35Q75; 35Q40 | |
| dc.title | The Dirac system on the Anti-de Sitter Universe | |
| dc.type | text |