Algebras of unbounded operators and physical applications: a survey

TL;DR

This survey reviews the mathematical structure of unbounded operator algebras and explores their significance in physical applications, especially in quantum mechanics of large systems.

Contribution

It provides a comprehensive overview of unbounded operator algebras and highlights their importance in modeling complex quantum systems, connecting mathematical theory with physical practice.

Findings

Unbounded operator algebras are fundamental in quantum mechanics.

The survey clarifies the mathematical foundations of these algebras.

Applications in large quantum systems are emphasized.

Abstract

After an historical introduction on the standard algebraic approach to quantum mechanics of large systems we review the basic mathematical aspects of the algebras of unbounded operators. After that we discuss in some details their relevance in physical applications.