A remark on the deformation of GNS representations of *-algebras

2000/12/11 by Stefan Waldmann · 5 citations
Mathematics · Physics and Astronomy · #Advanced Topics in Algebra #Algebra over a field #Algebraic number #Algebraic structures and combinatorial models #Classical limit #Deformation (meteorology) #Fock space #Homotopy and Cohomology in Algebraic Topology #Limit (mathematics) #Mathematical analysis #Mathematical physics #Mathematics #Physics #Pure mathematics #Quantization (signal processing) #Quantum #Quantum mechanics #Representation (politics) #Schrödinger's cat #math-ph #math.MP #math.QA #math.SG

paper · pdf · doi:10.1016/s0034-4877(01)80096-3

published in Reports on Mathematical Physics 48(3), 389-396 (Elsevier BV) · LaTeX2e, 8 pages

arxiv created 2000/12/11 · openalex publication_date 2001/12/01 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

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 Schrödinger representation as well as KMS functionals are discussed.

Citations

• Formal GNS Construction and WKB Expansion in Deformation Quantization
• Noncommutative Yang-Mills from equivalence of star products
• Noncommutative gauge theory for Poisson manifolds
• On the Deformation of Rings and Algebras
• Deformation Quantization of Poisson Manifolds
• A Path Integral Approach¶to the Kontsevich Quantization Formula