Quantizing Dirac and Nambu Brackets

TL;DR

This paper explores the relationship between classical and quantum Dirac and Nambu brackets, proposing Nambu brackets as a preferred method for quantum constraints despite some unconventional behaviors.

Contribution

It introduces a novel perspective on quantizing Dirac and Nambu brackets and discusses the advantages of using Nambu brackets for quantum constraints.

Findings

Classical relations shed light on the Jacobi identity for Dirac brackets.

Quantum Nambu brackets offer a promising approach for constraints.

Unorthodox behaviors are associated with quantum 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.