Structure of the Dirac bracket in classical mechanics

Abstract

We discuss the structure of the Dirac bracket in classical mechanics. We consider a generalization of the usual Poisson bracket and show the close connection of this generalization to the Lagrange brackets of classical mechanics. We show how the Dirac bracket appears as a particular case of the generalized Poisson bracket, thus giving a simple reason why the Jacobi identity holds for the Dirac bracket. We also discuss the nature of the transformations generated via the Dirac bracket and the relation of these to canonical transformations.