Elements of (super-)Hamiltonian Formalism

Abstract

In these lectures we discuss some basic aspects of Hamiltonian formalism, which usually do not appear in standard texbooks on classical mechanics for physicists. We pay special attention to the procedure of Hamiltonian reduction illustrating it by the examples related to Hopf maps. Then we briefly discuss the supergeneralisation(s) of the Hamiltonian formalism and present some simple models of supersymmetric mechanics on Kähler manifolds.

Lectures given at the Winter School on Modern Trends in Supersymmetric Mechanics, March 2005 Frascati; misprints corrected

References in corpus (5)

• N=8 supersymmetric mechanics on special Kähler manifolds
• Quantum Oscillator on $\DC P^n$ in a constant magnetic field
• Two-dimensional N=8 supersymmetric mechanics in superspace
• Oscillator potential for the four-dimensional Hall effect
• N=8 Supersymmetric Quaternionic Mechanics

Cited by in corpus (12)

• Covariant hamiltonian dynamics
• Second Hopf map and supersymmetric mechanics with Yang monopole
• Relationship between quantum mechanics with and without monopoles
• ${\mathbb{C}}^N$-Smorodinsky-Winternitz system in a constant magnetic field
• Hidden symmetry and (super)conformal mechanics in a monopole background
• Multi-center MICZ-Kepler systems
• Hopf maps and Wigner's little groups
• Two--center quantum MICZ--Kepler system and the Zeeman effect in the charge-dyon system
• Variational problem for Hamiltonian system on so(k, m) Lie-Poisson manifold and dynamics of semiclassical spin
• Integrable isotropic profiles for polarized light
• Landau problem on the ellipsoid, hyperboloid and paraboloid of revolution
• Reductions related with Hopf maps