Quantizing Dirac and Nambu Brackets

Abstract

We relate classical and quantum Dirac and Nambu brackets. At the classical level, we use the relations between the two brackets to gain some insight into the Jacobi identity for Dirac brackets, among other things. At the quantum level, we suggest that the Nambu bracket is the preferred method for introducing constraints, although at the expense of some unorthodox behavior, which we describe in detail.

Talk given by the first author at the Coral Gables Conference, 14 December 2002, Fort Lauderdale, Florida