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arXiv · 0706.1315

The Dirac system on the Anti-de Sitter Universe

Alain Bachelot
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Abstract

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.

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Alain Bachelot. 2008-02-25. The Dirac system on the Anti-de Sitter Universe. https://doi.org/10.1007/s00220-008-0564-8

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