Propagation estimates for Dirac operators and application to scattering theory
[Estimations de propagation pour des opérateurs de Dirac et application à la théorie de la diffusion]
Daudé, Thierry
Annales de l'Institut Fourier, Tome 54 (2004), p. 2021-2083 / Harvested from Numdam
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Dans cet article, nous prouvons plusieurs estimations de propagation pour une équation de Dirac massive en espace-temps plat. Ces estimations nous permettent de construire l'opérateur de vitesse asymptotique et de caractériser son spectre. En utilisant cette nouvelle information, nous obtenons des résultats complets de scattering. Précisèment, nous prouvons l'existence et la complétude asymptotique des opérateurs d'onde modifiés à la Dollard.

In this paper, we prove propagation estimates for a massive Dirac equation in flat spacetime. This allows us to construct the asymptotic velocity operator and to analyse its spectrum. Eventually, using this new information, we are able to obtain complete scattering results; that is to say we prove the existence and the asymptotic completeness of the Dollard modified wave operators.

Publié le : 2004-01-01
DOI : https://doi.org/10.5802/aif.2074
Classification:  35P25,  35Q40,  35B40,  81U99
Mots clés: Equations aux dérivées partielles, théorie spectrale, théorie de la diffusion, équation de Dirac, estimations de propagation, théorie de Mourre 
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     author = {Daud\'e, Thierry},
     title = {Propagation estimates for Dirac operators and application to scattering theory},
     journal = {Annales de l'Institut Fourier},
     volume = {54},
     year = {2004},
     pages = {2021-2083},
     doi = {10.5802/aif.2074},
     mrnumber = {2134232},
     zbl = {1080.35101},
     language = {en},
     url = {http://dml.mathdoc.fr/item/AIF_2004__54_6_2021_0}
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Daudé, Thierry. Propagation estimates for Dirac operators and application to scattering theory. Annales de l'Institut Fourier, Tome 54 (2004) pp. 2021-2083. doi : 10.5802/aif.2074. http://gdmltest.u-ga.fr/item/AIF_2004__54_6_2021_0/

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