The Kepler problem spinor regularization and pre-quantization of the negative-energy manifold

DOI10.1007/BF01560623zbMath0614.70004MaRDI QIDQ1819952

Maria Dina Vivarelli

Publication date: 1986

Published in: Meccanica (Search for Journal in Brave)

zbMATH Keywords

phase spaceKepler problemsymplectic manifoldHopf fibrationenergy levelscompact manifoldRunge-Lenz vectorpre-quantizationquantization proceduregeometric quantization procedureKustaanheimo- Stiefel regularizationnegative isoenergetic orbitspre-quantized manifoldspinor formulationstandard quantization condition

Mathematics Subject Classification ID

Two-body problems (70F05) General mathematical topics and methods in quantum theory (81Q99) Geometric quantization (53D50) Generalized coordinates; event, impulse-energy, configuration, state, or phase space for problems in mechanics (70G10)

Related Items (6)

The KS-transformation revisited ⋮ Reductions and quantization ⋮ Geometrical and physical outlook on the cross product of two quaternions ⋮ On the connection among three classical mechanical problems via the hypercomplex KS-transformation ⋮ On a first integral of the Kepler problem ⋮ The Kepler problem: A unifying view

Cites Work

• Geometry of spinor regularization
• A new regularization of the restricted three-body problem and an application
• Miscellanea from the history of celestial mechanics
• The KS-transformation in hypercomplex form
• Perturbation theory of Kepler motion based on spinor regularization.
• Regularization of kepler's problem and the averaging method on a manifold
• On nonclassical canonical systems
• On the regularization of the Kepler problem
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