Construction of the Noncommutative Complex Ball

TL;DR

This paper constructs a noncommutative version of the complex ball, a Hermitian symmetric space, using coherent state quantization, and explores a quantum field theory model on this noncommutative space.

Contribution

It introduces a novel noncommutative geometric construction of the complex ball and develops a related quantum field theory model.

Findings

Successful construction of the noncommutative complex ball

Recovery of the classical manifold in the commutative limit

Formulation of a quantum field theory on the noncommutative space

Abstract

We describe the construction of the noncommutative complex ball whose commutative analog is the Hermitian symmetric space $D=SU(m,1)/U(m)$, with the method of coherent state quantization. In the commutative limit we obtain the standard manifold. We consider also a quantum field theory model on the noncommutative manifold.