Homogeneous Fedosov star products on cotangent bundles. II: GNS representations, the WKB expansion, traces, and applications

DOI10.1016/S0393-0440(98)00041-2zbMath0989.53060arXivq-alg/9711016MaRDI QIDQ1299195

Martin Bordemann, Stefan Waldmann, Nikolai Alexander Neumaier

Publication date: 16 November 1999

Published in: Journal of Geometry and Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/q-alg/9711016

zbMATH Keywords

cotangent bundledeformation quantizationLagrangian submanifoldWKB expansionfixed-point setdifferential operator representationsformal GNS constructionhomogeneous star products of Weyl ordered type

Mathematics Subject Classification ID

Geometry and quantization, symplectic methods (81S10) Semiclassical techniques, including WKB and Maslov methods applied to problems in quantum theory (81Q20) Deformation quantization, star products (53D55)

Related Items (21)

On representations of star product algebras over cotangent spaces on Hermitian line bundles. ⋮ The Wentzel–Kramers–Brillouin approximation method applied to the Wigner function ⋮ *-IDEALS AND FORMAL MORITA EQUIVALENCE OF *-ALGEBRAS ⋮ Traces for Star Products on the Dual of a Lie Algebra ⋮ Deformation quantization and homological reduction of a lattice gauge model ⋮ Convergent star products on cotangent bundles of Lie groups ⋮ Notes on the \(L_\infty\)-approach to local gauge field theories ⋮ A COHOMOLOGICAL CONSTRUCTION OF MODULES OVER FEDOSOV DEFORMATION QUANTIZATION ALGEBRA ⋮ On conformal higher spins in curved background ⋮ STATES AND REPRESENTATIONS IN DEFORMATION QUANTIZATION ⋮ \(\mathcal W\) geometry from Fedosov's deformation quantization ⋮ Convergence of the Wick star product ⋮ Algebraic Rieffel induction, formal Morita equivalence, and applications to deformation quantization. ⋮ Low-energy effective action of \(N=2\) gauge multiplet induced by hypermultiplet matter ⋮ Wick quantization of cotangent bundles over Riemannian manifolds ⋮ A remark on the deformation of GNS representations of *-algebras ⋮ Fedosov quantization of Lagrange–Finsler and Hamilton–Cartan spaces and Einstein gravity lifts on (co) tangent bundles ⋮ Compatible symplectic connections on a cotangent bundle and the Fedosov quantization ⋮ Deformation quantization on the cotangent bundle of a Lie group ⋮ Deformation theory of Courant algebroids via the Rothstein algebra ⋮ Traces for star products on symplectic manifolds

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