Quantum Field Theory on quantized Bergman domain

TL;DR

This paper develops a quantized version of a Bergman domain using oscillator realizations of SU(2,2) representations, enabling a non-commutative scalar field formulation with star-product quantization.

Contribution

It introduces a novel oscillator-based realization of SU(2,2) discrete series and formulates a regularized non-commutative scalar field on the quantized domain.

Findings

Explicit formulas for the star-product quantization on the Bergman domain

A new oscillator realization of SU(2,2) discrete series

A framework for non-commutative scalar fields on quantized domains

Abstract

We present an oscillator realization of discrete series representations of group SU(2,2). We give formulas for the coherent state star-product quantization of a Bergman domain $D$. A formulation of a (regularized) non-commutative scalar field on a quantized $D$ is given.