Formal GNS Construction and WKB Expansion in Deformation Quantization

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.

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

Cited by in corpus (8)

• Homogeneous Fedosov Star Products on Cotangent Bundles I: Weyl and Standard Ordering with Differential Operator Representation
• A Remark on Formal KMS States in Deformation Quantization
• Homogeneous Fedosov Star Products on Cotangent Bundles II: GNS Representations, the WKB Expansion, and Applications
• Deformation Quantization of Hermitian Vector Bundles
• The Wentzel - Kramers - Brillouin approximation method applied to the Wigner function
• A Remark on the Deformation of GNS Representations of *-Algebras
• On representations of star product algebras over cotangent spaces on Hermitian line bundles
• Formal GNS Construction and States in Deformation Quantization