• Citer

Locality in GNS representations of deformation quantization

par Waldmann, Stefan
Référence Communications in Mathematical Physics, 210, 2, page (467-495)
Publication Publié, 2000-03

Article révisé par les pairs

• Détails
• Contenu

Résumé :

In the framework of deformation quantization we apply the formal GNS construction to find representations of the deformed algebras in pre-Hilbert spaces over ℂ[[λ]] and establish the notion of local operators in these pre-Hilbert spaces. The commutant within the local operators is used to distinguish "thermal" from "pure" representations. The computation of the local commutant is exemplified in various situations leading to the physically reasonable distinction between thermal representations and pure ones. Moreover, an analogue of von Neumann's double commutant theorem is proved in the particular situation of a GNS representation with respect to a KMS functional and for the Schrödinger representation on cotangent bundles. Finally we prove a formal version of the Tomita-Takesaki theorem.