Dirac versus reduced quantization and operator ordering

TL;DR

This paper demonstrates the equivalence between Dirac and reduced phase space quantization methods, showing how this equivalence determines the operator ordering of the Hamiltonian with illustrative examples.

Contribution

It establishes the connection between two quantization approaches and clarifies operator ordering issues through simple model examples.

Findings

Dirac and reduced quantization are equivalent methods.

Operator ordering is determined by this equivalence.

Examples illustrate specific operator orderings in simple models.

Abstract

We show an equivalence between Dirac quantization and the reduced phase space quantization. The equivalence of the both quantization methods determines the operator ordering of the Hamiltonian. Some examples of the operator ordering are shown in simple models.