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Examining Factors Using Standard Subspaces and Antiunitary Representations

Anderson, Paul
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.
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2023-05-01
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Undergraduate Honors Theses
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Clare, Pierre
Bolotnikov, Vladimir
Erlich, Joshua
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Mathematics
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https://scholarworks.wm.edu/handle/internal/11498
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