A natural map from a quantized space onto its semiclassical limit and a multi-parameter Poisson Weyl algebra

TL;DR

This paper constructs a natural map from a quantized algebra to its semiclassical limit and demonstrates it induces a homeomorphism between their spectra, linking quantum and classical algebraic structures.

Contribution

It introduces a natural map connecting quantized spaces to their semiclassical limits and proves it induces a homeomorphism between their spectra, advancing understanding of quantum-classical correspondence.

Findings

The natural map from quantized space to semiclassical limit is constructed.

The induced map is a homeomorphism between spectra.

Application to multi-parameter quantized Weyl algebra and Poisson spectrum.

Abstract

A natural map from a quantized space onto its semiclassical limit is obtained. As an application, we see that an induced map by the natural map is a homeomorphism from the spectrum of the multi-parameter quantized Weyl algebra onto the Poisson spectrum of its semiclassical limit.