Commutative Quantum Operator Algebras

Details Commutative Quantum Operator Algebras Commutative Quantum Operator Algebras

1995-01-13

arxiv.org/abs/q-alg/9501014v1

Physics

High Energy Physics

High Energy Physics - Theory

22 pages, Latex

Scientific paper

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.

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