Deformation Quantization and Irrational Numbers

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Publication details

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


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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