Central decomposition of Poincaré-invariant nets of local field algebras and absence of spontaneous breaking of the Lorentz group

Abstract

We study reducible, Poincare-invariant representations of nets of local field algebras and prove a number of structure results, some of which are generalizations of previous work on nets of observable algebras[l] and some of which are quite new. Using these we examine the central decomposition of such nets, study the spontaneous breaking of the Lorentz group symmetry under such decompositions into pure phases, and consider the significance of the modular automorphism groups of the wedge algebras On etudie des representations reductibles et Poincare invariantes de reseaux d'algebres de champs locales et on demontre des resultats de structure dont quelques-uns sont des generalisations d'un travail anterieur sur les reseaux d'algebres d'observables. En les employant on examine la decomposition centrale de tels reseaux, on etudie la brisure spontanee du groupe de Lorentz dans cette decomposition en phases pures, et on considere la signification des groupes d'automorphismes modulaires des algebres associees aux regions de l'espace-temps en forme de coin