[L'équation de Dirac sur l'univers Anti-de Sitter]
Nous cherchons des solutions globales de l'équation de Dirac dans l'univers Anti-de Sitter. Comme cet espace n'est pas globalement hyperbolique, le problème de Cauchy n'est pas, a priori, bien posé. Nous montrons que c'est toutefois le cas quand la masse du champ est grande par rapport à la constante cosmologique. En revanche, pour les faibles masses, nous construisons diverses conditions asymptotiques à l'infini, rendant le problème bien posé. Dans tous les cas, l'hamiltonien a un spectre discret. On établit également un résultat d'équipartition de l'énergie.
We investigate global solutions of the Dirac equation on the Anti-de-Sitter Universe. Since this space is not globally hyperbolic, the Cauchy problem is not, a priori, well-posed. Nevertheless, this is the case when the mass of the field is large compared to the cosmological constant. In opposite, for the light fermions, 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 get a result of equipartition of the energy.
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@article{CRMATH_2007__345_8_435_0,
author = {Alain Bachelot},
title = {The {Dirac} equation on the {Anti-de-Sitter} {Universe}},
journal = {Comptes Rendus. Math\'ematique},
pages = {435--440},
publisher = {Elsevier},
volume = {345},
number = {8},
year = {2007},
doi = {10.1016/j.crma.2007.09.011},
language = {en},
}
Alain Bachelot. The Dirac equation on the Anti-de-Sitter Universe. Comptes Rendus. Mathématique, Volume 345 (2007) no. 8, pp. 435-440. doi : 10.1016/j.crma.2007.09.011. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2007.09.011/
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Commentaires - Politique
New boundary conditions on the time-like conformal infinity of the Anti-de Sitter universe
Alain Bachelot
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