Construction of the noncommutative rank I Bergman domain

TL;DR

This paper develops a harmonic oscillator model for certain SU(2,1) group representations and applies coherent state quantization to the associated Bergman domain, advancing understanding of noncommutative geometry.

Contribution

It introduces a harmonic oscillator realization for degenerate discrete series of SU(2,1) and implements deformation quantization on the Bergman domain using coherent states.

Findings

Realization of SU(2,1) representations via harmonic oscillators

Deformation quantization of the Bergman domain

Application of coherent state quantization methods

Abstract

In this paper we present a harmonic oscillator realization of the most degenerate discrete series representations of the SU(2,1) group and the deformation quantization of the coset space $D=SU(2,1)/U(2)$ with the method of coherent state quantization.