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

Abstract

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{ö}dinger representation as well as KMS functionals are discussed.

LaTeX2e, 8 pages

References in corpus (4)

• D-branes and Deformation Quantization
• Operads and Motives in Deformation Quantization
• Noncommutative Yang-Mills from equivalence of star products
• Noncommutative gauge theory for Poisson manifolds

Cited by in corpus (2)

• States and representations in deformation quantization
• Some remarks on the GNS representations of topological ${}^{\ast }$-algebras