Mathematical Physics
[Submitted on 9 Jun 2007 (v1), last revised 25 Feb 2008 (this version, v3)]
Title:The Dirac system on the Anti-de Sitter Universe
View PDFAbstract: 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 $\Lambda>0$ : it appears a critical value, $\Lambda/12$, which plays a role similar to the Breitenlohner-Freedman bound for the scalar fields. When $M^2\geq \Lambda/12$ there exists a unique unitary dynamics. In opposite, for the light fermions satisfying $M^2<\Lambda/12$, 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.
Submission history
From: Alain Bachelot [view email][v1] Sat, 9 Jun 2007 15:38:15 UTC (26 KB)
[v2] Mon, 2 Jul 2007 13:55:00 UTC (28 KB)
[v3] Mon, 25 Feb 2008 11:10:24 UTC (32 KB)
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