Deformation quantization and irrational numbers

On Irrational and Transcendental Numbers

Representing numbers: prime and irrational

This article draws an analogy between prime and irrational numbers with respect to how these numbers are defined and how they are perceived by learners. Excerpts are presented from two research studies: a study on understanding prime numbers by pre-service elementary school teachers and a study on understanding irrational numbers by pre-service secondary school teachers. Considering the results...

Deformation Quantization

1. INTRODUCTION Quantum mechanics is often distinguished from classical mechanics by a statement to the effect that the observables in quantum mechanics, unlike those in classical mechanics, do not commute with one another. Yet classical mechanics is meant to give a description (with less precision) of the same physical world as is described by quantum mechanics. One mathematical transcription ...

Unsymmetrical Approximation of Irrational Numbers

1 A 1 < £ < , 5B B SB so that we have the classical theorem of Hurwitz. For other values of r, approximations from both sides are permitted, but the errors allowed on the two sides are different; hence the term unsymmetrical approximation. The result here was new, and is so related to Hurwitz's inequality that one side is strengthened and the other weakened. Notice that the result for r > l is ...

Deformation Quantization and Reduction

This note is an overview of the Poisson sigma model (PSM) and its applications in deformation quantization. Reduction of coisotropic and prePoisson submanifolds, their appearance as branes of the PSM, quantization in terms of L∞and A∞-algebras, and bimodule structures are recalled. As an application, an “almost” functorial quantization of Poisson maps is presented if no anomalies occur. This le...