[PDF] Analytic Continuation of Operators -- operators acting complex s-times -- Applications: from Number Theory and Group Theory to Quantum Field and String Theories | Semantic Scholar

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Corpus ID: 16787873

Analytic Continuation of Operators -- operators acting complex s-times -- Applications: from Number Theory and Group Theory to Quantum Field and String Theories

@article{Woon1997AnalyticCO,
title={Analytic Continuation of Operators -- operators acting complex s-times -- Applications: from Number Theory and Group Theory to Quantum Field and String Theories},
author={S. Woon},
journal={arXiv: High Energy Physics - Theory},
year={1997}
}

We are used to thinking of an operator acting once, twice, and so on. However, an operator acting integer times can be consistently analytic continued to an operator acting complex times. Applications: (s,r) diagrams and an extension of Fractional Calculus where commutativity of fractional derivatives is preserved, generating integrals and non-standard derivations of theorems in Number Theory, non-integer power series and breaking of Leibniz and Chain rules, pseudo-groups and symmetry deforming… Expand