Higher order first integrals of motion in a gauge covariant Hamiltonian framework

Abstract

The higher order symmetries are investigated in a covariant Hamiltonian formulation. The covariant phase-space approach is extended to include the presence of external gauge fields and scalar potentials. The special role of the Killing-Yano tensors is pointed out. Some non-trivial examples involving Runge-Lenz type conserved quantities are explicitly worked out.

13 pages, references added, accepted for publication in MPLA

References in corpus (9)

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Cited by in corpus (10)

• Hidden Symmetries of Dynamics in Classical and Quantum Physics
• Superintegrable systems on 3-dimensional curved spaces: Eisenhart formalism and separability
• Constants of Motion for Constrained Hamiltonian Systems: A Particle around a Charged Rotating Black Hole
• Conformal Killing Tensors and covariant Hamiltonian Dynamics
• Integrating Klein-Gordon-Fock equations in an external electromagnetic field on Lie groups
• Non-commutative oscillator with Kepler-type dynamical symmetry
• Goryachev-Chaplygin, Kovalevskaya, and Brdička-Eardley-Nappi-Witten pp-waves spacetimes with higher rank Stäckel-Killing tensors
• Hidden symmetries in a gauge covariant approach, Hamiltonian reduction and oxidation
• Covariant Approach of the Dynamics of Particles in External Gauge Fields, Killing Tensors and Quantum Gravitational Anomalies
• Gauge-covariant extensions of Killing tensors and conservation laws