The old frequency decomposition problem in the light of new quantization methods

TL;DR

This paper explores whether the traditional Klein-Gordon quantization approach can be used to understand the unique decomposition of the physical Hilbert space in refined algebraic quantization of constrained systems.

Contribution

It investigates the connection between classical frequency decomposition and modern quantization methods for constrained systems.

Findings

Identifies limitations of old frequency decomposition in modern quantization

Proposes a new perspective on the relationship between classical and quantum decompositions

Highlights potential for integrating old methods with new quantization techniques

Abstract

The question is raised whether the unique decomposition of the physical Hilbert space, as emerging in the refined algebraic quantization of a constrained system, may be understood in terms of the old Klein-Gordon type quantization.