Comparison and Continuity of Wick-type Star Products on certain coadjoint orbits
Chiara Esposito, Philipp Schmitt, Stefan Waldmann
TL;DR
This paper compares two constructions of Wick-type star products on coadjoint orbits, proves their equivalence, and establishes the continuity of the star product on the 2-sphere, enabling a Fréchet algebra completion.
Contribution
It demonstrates the equivalence of Alekseev-Lachowska and Karabegov star products and proves their continuity on the 2-sphere, a novel result in this context.
Findings
The star products by Alekseev-Lachowska and Karabegov agree on coadjoint orbits.
The star product on the 2-sphere is continuous.
The star product can be completed to a Fréchet algebra.
Abstract
In this paper we discuss continuity properties of the Wick-type star product on the 2-sphere, interpreted as a coadjoint orbit. Star products on coadjoint orbits in general have been constructed by different techniques. We compare the constructions of Alekseev-Lachowska and Karabegov and we prove that they agree in general. In the case of the 2-sphere we establish the continuity of the star product, thereby allowing for a completion to a Fr\'echet algebra.
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