no. 6
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, Thierry1
1 Université Bordeaux I, Institut de Mathématiques Appliquées de Bordeaux, UMR CNRS 5466, 351 cours de la libération, 33405 Talence Cedex (France)
Annales de l'Institut Fourier, Tome 54 (2004) no. 6, pp. 2021-2083.

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.

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.

DOI : 10.5802/aif.2074
Classification : 35P25, 35Q40, 35B40, 81U99
Keywords: Partial differential equations, spectral theory, scattering theory, Dirac's equation, propagation estimates, Mourre theory
Mots-clés : Equations aux dérivées partielles, théorie spectrale, théorie de la diffusion, équation de Dirac, estimations de propagation, théorie de Mourre

Daudé, Thierry 1

1 Université Bordeaux I, Institut de Mathématiques Appliquées de Bordeaux, UMR CNRS 5466, 351 cours de la libération, 33405 Talence Cedex (France) 
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Daudé, Thierry. Propagation estimates for Dirac operators and application to scattering theory. Annales de l'Institut Fourier, Tome 54 (2004) no. 6, pp. 2021-2083. doi : 10.5802/aif.2074. https://aif.centre-mersenne.org/articles/10.5802/aif.2074/

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