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Commutative Quantum Operator Algebras
A key notion bridging the gap between {\it quantum operator algebras}
\cite{LZ10} and {\it vertex operator algebras} \cite{Bor}\cite{FLM} is the
definition of the commutativity of a pair of quantum operators (see section 2
below). This is not commutativity in any ordinary sense, but it is clearly the
correct generalization to the quantum context. The main purpose of the current
paper is to begin laying the foundations for a complete mathematical theory of
{\it commutative quantum operator algebras.} We give proofs of most of the
relevant results announced in \cite{LZ10}, and we carry out some calculations
with sufficient detail to enable the interested reader to become proficient
with the algebra of commuting quantum operators.Comment: 22 pages, Late
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