Date Thesis Awarded

5-2023

Access Type

Honors Thesis -- Open Access

Degree Name

Bachelors of Science (BS)

Department

Mathematics

Advisor

Pierre Clare

Committee Members

Vladimir Bolotnikov

Joshua Erlich

Abstract

In an effort to provide an axiomization of quantum mechanics, John von Neumann and Francis Joseph Murray developed many tools in the theory of operator algebras. One of the many objects developed during the course of their work was the von Neumann algebra, originally called a ring of operators. The purpose of this thesis is to give an overview of the classification of elementary objects, called factors, and explore connections with other mathematical objects, namely standard subspaces in Hilbert spaces and antiunitary representations. The main results presented here illustrate instances of these interconnections that are relevant in Algebraic Quantum Field Theory and point to potential further connections, currently unexplored.

Recommended Citation

Anderson, Paul, "Examining Factors Using Standard Subspaces and Antiunitary Representations" (2023). Undergraduate Honors Theses. William & Mary. Paper 2029.
https://scholarworks.wm.edu/honorstheses/2029