Towards asymptotic completeness of two-particle scattering in local relativistic QFT - Archive ouverte HAL Accéder directement au contenu
Article Dans Une Revue Communications in Mathematical Physics Année : 2014

Towards asymptotic completeness of two-particle scattering in local relativistic QFT

Résumé

We consider the problem of existence of asymptotic observables in local relativistic theories of massive particles. Let $\ti p_1$ and $\ti p_2$ be two energy-momentum vectors of a massive particle and let $\De$ be a small neighbourhood of $\ti p_1+\ti p_2$. We construct asymptotic observables (two-particle Araki-Haag detectors), sensitive to neutral particles of energy-momenta in small neighbourhoods of $\ti p_1$ and $\ti p_2$. We show that these asymptotic observables exist, as strong limits of their approximating sequences, on all physical states from the spectral subspace of $\De$. Moreover, the linear span of the ranges of all such asymptotic observables coincides with the subspace of two-particle Haag-Ruelle scattering states with total energy-momenta in $\De$. The result holds under very general conditions which are satisfied, for example, in $\la \phi^4_2$. The proof of convergence relies on a variant of the phase-space propagation estimate of Graf.
Fichier principal
Vignette du fichier
detectors-final.pdf (283.72 Ko) Télécharger le fichier
Origine Fichiers produits par l'(les) auteur(s)
Loading...

Dates et versions

hal-00752083 , version 1 (14-11-2012)
hal-00752083 , version 2 (15-11-2012)
hal-00752083 , version 3 (20-11-2012)

Identifiants

Citer

Wojciech Dybalski, Christian Gérard. Towards asymptotic completeness of two-particle scattering in local relativistic QFT. Communications in Mathematical Physics, 2014, Commun. Math. Phys. 326:81–109 (2014), 326 (1). ⟨hal-00752083v3⟩
101 Consultations
195 Téléchargements

Altmetric

Partager

Gmail Mastodon Facebook X LinkedIn More