Reduction Procedures in Classical and Quantum Mechanics

TL;DR

This paper provides a pedagogical overview of reduction procedures in classical and quantum mechanics, highlighting their similarities and differences in algebraic and geometrical frameworks.

Contribution

It offers a comprehensive comparison of reduction methods in classical and quantum contexts, emphasizing their core principles and distinctions.

Findings

Clarifies the algebraic and geometrical aspects of reduction procedures

Highlights analogies and differences between classical and quantum reductions

Provides pedagogical insights into the application of reduction methods

Abstract

We present, in a pedagogical style, many instances of reduction procedures appearing in a variety of physical situations, both classical and quantum. We concentrate on the essential aspects of any reduction procedure, both in the algebraic and geometrical setting, elucidating the analogies and the differences between the classical and the quantum situations.