Dirac versus reduced phase space quantization for systems admitting no gauge conditions

TL;DR

This paper compares Dirac and reduced phase space quantization methods for systems without gauge conditions, highlighting their similarities, differences, and the interpretation of gauge degrees of freedom in such constrained Hamiltonian systems.

Contribution

It develops methods for quantizing systems without gauge conditions and analyzes the relationship between Dirac and reduced phase space quantizations for specific spin models.

Findings

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

Some constrained systems can only be quantized using the Dirac method.

A new interpretation of gauge degrees of freedom is proposed.

Abstract

The constrained Hamiltonian systems admitting no gauge conditions are considered. The methods to deal with such systems are discussed and developed. As a concrete application, the relationship between the Dirac and reduced phase space quantizations is investigated for spin models belonging to the class of systems under consideration. It is traced out that the two quantization methods may give similar, or essentially different physical results, and, moreover, a class of constrained systems, which can be quantized only by the Dirac method, is discussed. A possible interpretation of the gauge degrees of freedom is given.