Théorie de la diffusion pour le modèle de Nelson et problème infrarouge
Journées équations aux dérivées partielles (2003), article no. 7, 13 p.

Nous considérons dans cet exposé la théorie de la diffusion pour des modèles de Pauli-Fierz sans masse divergents infrarouge. Nous montrons que les représentations CCR obtenues a partir des champs asymptotiques contiennent des secteurs cohérents décrivant un nombre infini de bosons asymptotiquement libres. Nous formulons quelques conjectures qui conduisent a une notion bien définie de sections efficaces inclusives et non inclusives pour les Hamiltoniens de Pauli-Fierz. Finalement nous donnons une description générale de la théorie de la diffusion pour des modèles de théorie quantique des champs en présence de secteurs cohérents pour les représentations CCR asymptotiques.

We consider in this paper the scattering theory of infrared divergent massless Pauli-Fierz hamiltonians. We show that the CCR representations obtained from the asymptotic field contain so-called coherent sectors describing an infinite number of asymptotically free bosons. We formulate some conjectures leading to mathematically well defined notion of inclusive and non-inclusive scattering cross-sections for Pauli-Fierz Hamiltonians. Finally we give a general description of the scattering theory of QFT models in the presence of coherent sectors for the asymptotic CCR representations.

@article{JEDP_2003____A7_0,
     author = {G\'erard, Christian},
     title = {Th\'eorie de la diffusion pour le mod\`ele de Nelson et probl\`eme infrarouge},
     journal = {Journ\'ees \'equations aux d\'eriv\'ees partielles},
     eid = {7},
     publisher = {Universit\'e de Nantes},
     year = {2003},
     doi = {10.5802/jedp.621},
     zbl = {02079442},
     mrnumber = {2050593},
     language = {fr},
     url = {http://www.numdam.org/articles/10.5802/jedp.621/}
}
Gérard, Christian. Théorie de la diffusion pour le modèle de Nelson et problème infrarouge. Journées équations aux dérivées partielles (2003), article  no. 7, 13 p. doi : 10.5802/jedp.621. http://www.numdam.org/articles/10.5802/jedp.621/

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