Quantum Number Theory

Author: Kenji Tokuo¹

Source: International Journal of Theoretical Physics, Volume 43, Number 12, December 2004 , pp. 2461-2481(21)

Publisher: Springer

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Abstract:

This paper shows that a theory of numbers can be developed within the framework of typed quantum logic. First, the core system of typed quantum logic is stated precisely, on which a theory of numbers is to be built. Second, under a minimal additional assumption about natural number objects, a step-by-step description of quantum real numbersis provided. Finally, it is suggested that the “quantum reals” are modeled by the “observables” in terms of quantum physics.

Keywords: Quantum logic; type theory; theory of numbers

Document Type: Research article

DOI: 10.1007/s10773-004-7711-6

Affiliations: 1: Graduate School of Human and Environmental Studies, Kyoto University, Kyoto, Japan, Email: tokuo@math.h.kyoto-u.ac.jp

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