A quantum twistor bundle

TL;DR

This paper constructs and analyzes a quantum twistor bundle as a noncommutative geometric object, extending classical bundle concepts into the quantum realm with detailed algebraic and $C^*$-algebraic descriptions.

Contribution

It introduces a quantum twistor bundle as a $U(1)$-quotient of a quantum instanton bundle, fulfilling algebraic conditions and providing a detailed $C^*$-algebraic description.

Findings

Explicit $C^*$-algebra of the quantum twistor bundle

Verification of algebraic conditions for noncommutative bundles

Extension of classical bundle concepts to quantum setting

Abstract

We investigate a quantum twistor bundle constructed as a $U(1)$-quotient of the quantum instanton bundle of Bonechi, Ciccoli and Tarlini. It is an example of a noncommutative bundle fulfilling conditions of the purely algebraic framework proposed by Brzezi\'{n}ski and Szyma\'{n}ski. We provide a detailed description of the corresponding $C^*$-algebra of `continuous functions' on its noncommutative total space.