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• W3098481547 abstract "In the framework of deformation quantization we apply the formal GNS construction to find representations of the deformed algebras in pre-Hilbert spaces over $mathbb C[[lambda]]$ 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 Schrodinger representation on cotangent bundles. Finally we prove a formal version of the Tomita-Takesaki theorem." @default.
• W3098481547 created "2020-11-23" @default.
• W3098481547 creator A5007294217 @default.
• W3098481547 date "2000-03-01" @default.
• W3098481547 modified "2023-09-27" @default.
• W3098481547 title "Locality in GNS Representations of Deformation Quantization" @default.
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• W3098481547 doi "https://doi.org/10.1007/s002200050788" @default.
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