A Remark on the Deformation of GNS Representations of *-Algebras

Details A Remark on the Deformation of GNS Representations of *-Algebras A Remark on the Deformation of GNS Representations of *-Algebras

2000-12-11

arxiv.org/abs/math/0012071v1

Rept.Math.Phys. 48 (2001) 389-396

Mathematics

Quantum Algebra

LaTeX2e, 8 pages

Scientific paper

10.1016/S0034-4877(01)80096-3

Motivated by deformation quantization we investigate the algebraic GNS construction of *-representations of deformed *-algebras over ordered rings and compute their classical limit. The question if a GNS representation can be deformed leads to the deformation of positive linear functionals. Various physical examples from deformation quantization like the Bargmann-Fock and the Schr{\"o}dinger representation as well as KMS functionals are discussed.

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