Killing tensors and canonical geometry

Abstract

The systematic derivation of constants of the motion, based on Killing tensors and the gauge covariant approach, is outlined. Quantum dots are shown to support second-, third- and fourth-rank Killing tensors.

14 pages, no figures. v3: Introduction and Conclusion rewritten, new section on algebraic properties and more reference added. Accepted for publication in Classical and Quantum Gravity

References in corpus (3)

• Covariant hamiltonian dynamics
• Quantum integrability of quadratic Killing tensors
• Constants of Motion for Constrained Hamiltonian Systems: A Particle around a Charged Rotating Black Hole

Cited by in corpus (20)

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• Notes on Super Killing Tensors
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• On integrability of the Killing equation
• New currents with Killing-Yano tensors
• Eisenhart Lift of $2$--Dimensional Mechanics
• Self-dual metrics with maximally superintegrable geodesic flows
• Conformal symmetry for relativistic point particles
• Killing-Yano Cotton Currents
• Scale invariance and constants of motion
• Invariant prolongation of the Killing tensor equation
• Killing Tensors in Koutras-McIntosh Spacetimes
• Some metrics admitting nonpolynomial first integrals of the geodesic equation
• Schouten-Codazzi Gravity
• Gauge-covariant extensions of Killing tensors and conservation laws
• The Bohlin variant of the Eisenhart lift