Journal of Symplectic Geometry

Volume 12 (2014)

Number 1

Deformation quantization and irrational numbers

Pages: 1 – 22

DOI: http://dx.doi.org/10.4310/JSG.2014.v12.n1.a1

Authors

Eli Hawkins (Department of Mathematics, The University of York, Heslington, York, United Kingdom)

Alan Haynes (Department of Mathematics, The University of York, Heslington, York, United Kingdom)

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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