Dirac's Constrained Hamiltonian Dynamics from an Unconstrained Dynamics

TL;DR

This paper derives Dirac's Hamiltonian equations for constrained systems from unconstrained dynamics using a limiting process, clarifying the role of primary constraints and their time persistence.

Contribution

It introduces a novel derivation of Dirac's constrained Hamiltonian equations from unconstrained systems, highlighting the significance of primary constraints.

Findings

Primary constraints are essential in the Hamiltonian formulation.

The derivation clarifies how constraints persist over time.

The approach provides insight into the structure of constrained dynamics.

Abstract

We derive the Hamilton equations of motion for a constrained system in the form given by Dirac, by a limiting procedure, starting from the Lagrangean for an unconstrained system. We thereby ellucidate the role played by the primary constraints and their persistance in time.