Quantization on a manifold with connection

DOI10.1063/1.523913zbMath0426.58011OpenAlexW2015562971MaRDI QIDQ3862131

J. Underhill

Publication date: 1978

Published in: Journal of Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1063/1.523913

zbMATH Keywords

quantizationaffine connectioncorrespondence principleWeyl correspondencemanifolds as configuration spacePoisson bracket Lie algebra of classical observables

Mathematics Subject Classification ID

General mathematical topics and methods in quantum theory (81Q99) Commutation relations and statistics as related to quantum mechanics (general) (81S05) Geometric quantization (53D50)

Related Items (15)

Weyl transformations on manifolds I. Definitions and isomorphism theorems ⋮ Quantum integrable systems constrained on the sphere ⋮ Canonical quantization of constants of motion ⋮ Weyl quantization of degree 2 symplectic graded manifolds ⋮ Strict deformation quantization of a particle in external gravitational and Yang-Mills fields ⋮ Equivalence of extrinsic and intrinsic quantization for observables not preserving the vertical polarization ⋮ Equivalence of Dirac and intrinsic quantization for non-free group actions ⋮ Weyl transformations on manifolds. II: Generalized trace and inverse mapping formula ⋮ Segal-Bargmann transforms from hyperbolic Hamiltonians ⋮ Bloch theory and quantization of magnetic systems ⋮ Homogeneous Fedosov star products on cotangent bundles. II: GNS representations, the WKB expansion, traces, and applications ⋮ Quantization and commutative superalgebras ⋮ Deformation quantization on cotangent bundles ⋮ Deformation quantization on the cotangent bundle of a Lie group ⋮ Quantization of the conformal Kepler problem and its application to the hydrogen atom

Cites Work

• Quantization as deformation theory

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