Deformation Quantization and Irrational Numbers

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JournalJournal of Symplectic Geometry
DateAccepted/In press - 2011
DatePublished (current) - 2014
Issue number1
Volume12
Number of pages22
Original languageEnglish

Abstract

Diophantine approximation is the problem of approximating a real number by rational numbers. We propose a version of this in which the numerators are approximately related to the denominators by a Laurent polynomial. Our definition is motivated by the problem of constructing strict deformation quantizations of symplectic manifolds. We show that this type of approximation exists for any real number and also investigate what happens if the number is rational or a quadratic irrational.

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