Twist-Deformed Lorentzian Heisenberg-Algebras

TL;DR

This paper introduces a method to deform Lorentzian Heisenberg algebras using twist formalism, leading to high-energy extensions of quantum mechanics with minimal uncertainty properties for spacetime measurements.

Contribution

It presents a novel double twist deformation approach to Minkowskian Heisenberg-algebras and their quantizations, extending relativistic quantum mechanics at high energies.

Findings

Double twist deformations produce generalized Lorentzian Heisenberg-algebras.

Deformed algebras enable minimal uncertainty in high-energy spacetime measurements.

The procedure is exemplified with a concrete case.

Abstract

The Moyal-Weyl quantization procedure is embedded into the twist formalism of vector fields on phase space. Double application of twists provide most general deformations of Minkowskian Heisenberg-algebras and corresponding quantizations of the Lorentz-algebra. Such deformations deliver high-energy extensions of standard relativistic quantum mechanics. These are required to obtain minimal uncertainty properties for high-energy spacetime measurements that standard quantum mechanics lacks. The procedure of double twist application is outlined. We give an instructive and genuine example.