Commutative Quantum Operator Algebras
Abstract
A key notion bridging the gap between quantum operator algebras LZ10 and vertex operator algebras BorFLM 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 commutative quantum operator algebras. We give proofs of most of the relevant results announced in 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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