Deformation quantization and irrational numbers (Q2510083)

This paper proposes a version of Diophantine approximation which can be useful to construct strict deformation quantization. First, the authors give a definition of an order-\(N\) rational approximation to a real number. Then, they motivate their definition by explaining how their work can be used in the theory of strict deformation quantization. They show how rational approximation arises from the construction of the deformation. Finally, they consider rational approximations and give a classification. They study both the rational case and the quadratic irrational case. Unanswered questions are also discussed.