Quantum twistors

TL;DR

This paper constructs an explicit star product on Minkowski space using twistor formalism, deforming the conformal spacetime via quantum group substitution, advancing the mathematical framework of quantum geometry.

Contribution

It introduces a new explicit star product on Minkowski space based on quadratic Poisson brackets and quantum group deformation within the twistor formalism.

Findings

Explicit star product on Minkowski space derived

Deformation of conformal spacetime via quantum group

Quantization achieved through twistor formalism

Abstract

We compute explicitly a star product on the Minkowski space whose Poisson bracket is quadratic. This star product corresponds to a deformation of the conformal spacetime, whose big cell is the Minkowski spacetime. The description of Minkowski space is made in the twistor formalism and the quantization follows by substituting the classical conformal group by a quantum group.