Relativistic Corrections to the Moyal-Weyl Spacetime

TL;DR

This paper introduces a relativistic version of the Moyal-Weyl spacetime by applying a deformation procedure inspired by quantum plane emergence, resulting in a spacetime with relativistic corrections.

Contribution

It develops a quantum field theory-inspired coordinate operator to deform spacetime, incorporating relativistic effects into the Moyal-Weyl framework.

Findings

Relativistic corrections modify the standard Moyal-Weyl plane.

A new deformation procedure based on quantum plane emergence.

The resulting spacetime differs from the classical Moyal-Weyl plane.

Abstract

We define a coordinate operator in a QFT-fashion to obtain by a deformation procedure a relativistic Moyal-Weyl spacetime. The idea is extracted from recent progress in deformation theory concerning the emergence of the quantum plane of the Landau-quantization. The obtained spacetime is not equal to the standard Moyal-Weyl plane but relativistic corrections occur.