Formal GNS Construction and WKB Expansion in Deformation Quantization

1996/11/04 by Martin Bordemann, M. Bordemann, Stefan Waldmann +3 · 1 citation
Engineering · Mathematics · Medicine · Physics and Astronomy · #FOS: Mathematics #Geophysics and Sensor Technology #Medical Imaging Techniques and Applications #Quantum Algebra (math.QA) #Quantum Mechanics and Non-Hermitian Physics #math.QA #q-alg

paper · pdf · doi:10.48550/arxiv.q-alg/9611004

LaTeX 2.09, 5 pages; Contribution to the Ascona Meeting on Deformation Theory, Symplectic Geometry, and Applications, June 16-22, 1996

arxiv created 1996/11/04 · openalex publication_date 1996/11/04 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this contribution we review the formal GNS construction developped in a previous preprint (q-alg/9607019), and formulate the usual WKB-expansion in flat 2n-dimensional phase space in terms of a GNS construction with a positive linear functional with support on a projectable Lagrangean submanifold defined as a graph of an exact one form dS. The main trick is a suitable form of the star-exponential of S.

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• Homogeneous Fedosov Star Products on Cotangent Bundles II: GNS Representations, the WKB Expansion, and Applications
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