The Fuzzy Kaehler Coset Space with the Darboux Coordinates
Shogo Aoyama, Takahiro Masuda (Shizuoka University)
TL;DR
This paper explores the Fedosov deformation quantization on symplectic manifolds, identifying conditions under which the star product simplifies to the Moyal product using Darboux coordinates, and studies the fuzzy algebrae of Kaehler coset spaces.
Contribution
It introduces a class of differential forms r that make the star product equivalent to the Moyal product in Darboux coordinates, preserving invariance under canonical transformations.
Findings
Identified conditions for the star product to become Moyal product
Analyzed the fuzzy algebrae of Kaehler coset spaces
Established invariance properties under coordinate transformations
Abstract
The Fedosov deformation quantization of the symplectic manifold is determined by a 1-form differential r. We identify a class of r for which the product becomes the Moyal product by taking appropriate Darboux coordinates, but invariant by canonically transforming the coordinates. This respect of the product is explained by studying the fuzzy algebrae of the Kaehler coset space.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.