A Proof of Haag-Swieca's Compactness Property for Elastic Scattering States |
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Authors: | Jacques Bros |
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Affiliation: | (1) Service de Physique Théorique, CEA-Saclay, 91191 Gif-sur-Yvette, France. E-mail: bros@spht.saclay.cea.fr, FR |
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Abstract: | It is proved that in any massive relativistic quantum field theory satisfying two-particle asymptotic completeness, all the bounded energy components in the elastic two-particle range of all subsets of states which are excitations of the vacuum state by uniformly bounded observables localized in a given finite region of spacetime are compact in the Hilbert space of states. This result, which is in agreement with Haag-Swieca's conjecture, is also given a more precise form in terms of the rate of decrease of the ``N–dimensional thickness' (or approximation number) of such sets of states when N tends to infinity. A similar computation, valid at arbitrarily high energies, is also given for the massive free-field case. Received: 7 February 2003 / Accepted: 5 April 2003 Published online: 13 May 2003 Communicated by H. Araki, D. Buchholz and K. Fredenhagen |
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