Deformation Quantization and Irrational Numbers

Details Deformation Quantization and Irrational Numbers Deformation Quantization and Irrational Numbers

2011-05-27

arxiv.org/abs/1105.5541v1

Mathematics

Number Theory

20 pages

Scientific paper

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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