Formal GNS Construction and WKB Expansion in Deformation Quantization

Details Formal GNS Construction and WKB Expansion in Deformation Quantization Formal GNS Construction and WKB Expansion in Deformation Quantization

1996-11-04

arxiv.org/abs/q-alg/9611004v1

Mathematics

Quantum Algebra

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

Scientific paper

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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