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.
Keywords: Partial differential equations, spectral theory, scattering theory, Dirac's equation, propagation estimates, Mourre theory
Mot clés : Equations aux dérivées partielles, théorie spectrale, théorie de la diffusion, équation de Dirac, estimations de propagation, théorie de Mourre
@article{AIF_2004__54_6_2021_0, author = {Daud\'e, Thierry}, title = {Propagation estimates for {Dirac} operators and application to scattering theory}, journal = {Annales de l'Institut Fourier}, pages = {2021--2083}, publisher = {Association des Annales de l{\textquoteright}institut Fourier}, volume = {54}, number = {6}, year = {2004}, doi = {10.5802/aif.2074}, mrnumber = {2134232}, zbl = {1080.35101}, language = {en}, url = {http://www.numdam.org/articles/10.5802/aif.2074/} }
TY - JOUR AU - Daudé, Thierry TI - Propagation estimates for Dirac operators and application to scattering theory JO - Annales de l'Institut Fourier PY - 2004 SP - 2021 EP - 2083 VL - 54 IS - 6 PB - Association des Annales de l’institut Fourier UR - http://www.numdam.org/articles/10.5802/aif.2074/ DO - 10.5802/aif.2074 LA - en ID - AIF_2004__54_6_2021_0 ER -
%0 Journal Article %A Daudé, Thierry %T Propagation estimates for Dirac operators and application to scattering theory %J Annales de l'Institut Fourier %D 2004 %P 2021-2083 %V 54 %N 6 %I Association des Annales de l’institut Fourier %U http://www.numdam.org/articles/10.5802/aif.2074/ %R 10.5802/aif.2074 %G en %F AIF_2004__54_6_2021_0
Daudé, Thierry. Propagation estimates for Dirac operators and application to scattering theory. Annales de l'Institut Fourier, Volume 54 (2004) no. 6, pp. 2021-2083. doi : 10.5802/aif.2074. http://www.numdam.org/articles/10.5802/aif.2074/
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