Dirac versus reduced phase space quantization

TL;DR

This paper compares Dirac and reduced phase space quantization methods for certain Hamiltonian systems, revealing their similarities, differences, and conditions under which only the Dirac method is applicable, with implications for gauge degrees of freedom.

Contribution

It analyzes the relationship between Dirac and reduced phase space quantizations, identifying when they yield similar or different results and highlighting systems only quantizable via the Dirac method.

Findings

Dirac and reduced phase space quantizations can produce similar or different results.

Some constrained systems are only quantizable using the Dirac method.

A new interpretation of gauge degrees of freedom is proposed.

Abstract

The relationship between the Dirac and reduced phase space quantizations is investigated for spin models belonging to the class of Hamiltonian systems having no gauge conditions. It is traced out that the two quantization methods may give similar, or essentially different physical results, and, moreover, it is shown that there is a class of constrained systems, which can be quantized only by the Dirac method. A possible interpretation of the gauge degrees of freedom is given.