Lecture notes on operator algebras and their application in physics

TL;DR

This paper provides an introductory overview of operator algebras, specifically Banach- and C*-algebras, and explores their applications in physics, aimed at graduate mathematics students interested in quantum mechanics foundations.

Contribution

It offers a concise, accessible introduction to operator algebras and their relevance in physics, bridging functional analysis and quantum theory for graduate students.

Findings

Introduces Banach- and C*-algebras in a clear, simplified manner.

Connects operator algebras to foundational aspects of quantum mechanics.

Serves as an educational resource for mathematics students in physics applications.

Abstract

Lecture notes to a one-term course on operator algebras and their application in physics. Very brief and basic introduction to the subject of Banach- and C-star algebras complemented with their appearance in physics. The course is intended at mathematics students in their master program with a basic knowledge of functional analysis and some interest in the foundations of quantum mechanics.