Hyper-Hamiltonian dynamics

2002/04/09 by Giuseppe Gaeta, G. Gaeta, Paola Morando +1
Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #Classical mechanics #Covariant Hamiltonian field theory #Hamiltonian (control theory) #Hamiltonian mechanics #Hamiltonian system #Homotopy and Cohomology in Algebraic Topology #Integrable system #Mathematical optimization #Mathematical physics #Mathematics #Nonlinear Waves and Solitons #Phase space #Physics #Quantum mechanics #Superintegrable Hamiltonian system #math-ph #math.DS #math.MP #msc:37J99 #msc:53D99 #msc:70H99

paper · pdf · doi:10.1088/0305-4470/35/17/308

published as J. Phys. A 35 (2002), 3925-3943 · 24 pages; to appear in J. Phys. A

arxiv created 2002/04/09 · openalex publication_date 2002/04/19 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

We introduce an extension of Hamiltonian dynamics, defined on hyper-Kahler manifolds, which we call `hyper-Hamiltonian dynamics'. We show that this has many of the attractive features of standard Hamiltonian dynamics. We also discuss the prototypical integrable hyper-Hamiltonian systems, i.e. quaternionic oscillators.

Citations

• Lectures on Symplectic Geometry
• The Self-Duality Equations on a Riemann Surface
• Quaternionic K�hler manifolds
• Quaternionic Hamilton equations
• The Geometry and Dynamics of Magnetic Monopoles
• Twistor theory: An approach to the quantisation of fields and space-time
• Supersymmetric σ-models, twistors, and the Atiyah-Hitchin metric
• On the Dirac Theory of Spin 1/2 Particles and Its Non-Relativistic Limit
• Métriques kählériennes et fibrés holomorphes