Elements of (super-)Hamiltonian Formalism

TL;DR

This paper explores fundamental aspects of Hamiltonian formalism, including reduction techniques and supergeneralizations, with examples from Hopf maps and supersymmetric mechanics on Kähler manifolds.

Contribution

It provides a detailed discussion of Hamiltonian reduction and introduces supersymmetric extensions, which are often omitted in standard classical mechanics textbooks.

Findings

Illustration of Hamiltonian reduction via Hopf maps

Introduction of supersymmetric models on Kähler manifolds

Clarification of supergeneralizations of 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 K\"ahler manifolds.