Mathematical Physics

    

Real Numbers: a New (Quantum) Look, with a Hierarchical Structure

Authors: Lucian M. Ionescu

Rational numbers Q have much more structure beyond the ordered field structure which leads to Real Numbers as a metric completion.The modular group representation of continued fractions is used as a Number Theory "friendly" implementation of the real numbers, with a possible unification with p-adic numbers, beyond the "direct sum" adeles framework. This approach also allows to extend Fourier and Haar Wavelet Analysis, by including inversion as a geometric antipode. Other applications in Mathematical-Physics steam from the central role of the modular group: Belyi maps, Farey graphs and tessellations etc. which allow the study of important classes of numbers (algebraic, periods) in a systematic way. The presentation is a preliminary version the project, stating the motivation, goals and approach.

Comments: 36 Pages. Presentation in the ISU Pure and Applied Mathematics Seminar

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Submission history

[v1] 2023-11-01 21:32:59

Unique-IP document downloads: 211 times

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