Hamilton's Formalism for Systems with Constraints

TL;DR

This paper reviews Hamiltonian formalism for classical systems with constraints, focusing on gauge theories, local symmetries, and the connection between Lagrangian and Hamiltonian approaches.

Contribution

It provides a comprehensive introduction to Hamiltonian formalism for constrained systems, emphasizing the relation between symmetries and constraints in gauge theories.

Findings

Clarifies the relation between local symmetries and constraints

Explains the connection between Lagrangian and Hamiltonian symmetries

Provides a systematic review of Hamiltonian formalism for constrained systems

Abstract

The main goal of these lectures is to introduce and review the Hamiltonian formalism for classical constrained systems and in particular gauge theories. Emphasis is put on the relation between local symmetries and constraints and on the relation between Lagrangean and Hamiltonian symmetries.